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Research on deformations of real and complex manifolds and variations of invariants

Research Project

Project/Area Number 17204010
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionTokyo Institute of Technology

Principal Investigator

SHIGA Hiroshige  Tokyo Institute of Technology, 大学院・理工学研究科, 教授 (10154189)

Co-Investigator(Kenkyū-buntansha) AIKAWA Hiroaki  北海道大学, 大学院・理学研究科, 教授 (20137889)
SUGAWA Toshiyuki  東北大学, 大学院・情報科学研究科, 教授 (30235858)
村田 實  東京工業大学, 大学院・理工学研究科, 教授 (50087079)
野口 潤次郎  東京大学, 大学院・数理科学研究科, 教授 (20033920)
宮嶋 公夫  鹿児島大学, 理学部, 教授 (40107850)
今吉 洋一  大阪市立大学, 大学院・理学研究科, 教授 (30091656)
宍倉 光広  京都大学, 大学院・理学研究科, 教授 (70192606)
Co-Investigator(Renkei-kenkyūsha) MURATA Minoru  東京工業大学, 大学院・理工学研究科, 教授 (50087079)
MATSUZAKI Katsuhiko  岡山大学, 大学院・自然科学研究科, 教授 (80222298)
NOGUCHI Junjiro  東京大学, 大学院・数理科学研究科, 教授 (20033920)
MIYAJIMA Kimio  鹿児島大学, 理学部, 教授 (40107850)
IMAYOSHI Yoichi  大阪市立大学, 大学院・理学研究科, 教授 (30091656)
SHISHIKURA Mitsuhiro  京都大学, 大学院・理学研究科, 教授 (70192606)
SUMI Hiroki  大阪大学, 大学院・理学研究科, 准教授 (40313324)
Project Period (FY) 2005 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥27,300,000 (Direct Cost: ¥21,000,000、Indirect Cost: ¥6,300,000)
Fiscal Year 2008: ¥7,280,000 (Direct Cost: ¥5,600,000、Indirect Cost: ¥1,680,000)
Fiscal Year 2007: ¥5,850,000 (Direct Cost: ¥4,500,000、Indirect Cost: ¥1,350,000)
Fiscal Year 2006: ¥5,850,000 (Direct Cost: ¥4,500,000、Indirect Cost: ¥1,350,000)
Fiscal Year 2005: ¥8,320,000 (Direct Cost: ¥6,400,000、Indirect Cost: ¥1,920,000)
Keywords函数論 / タイヒミュラー空間 / 複素多様体 / ポテンシャル論 / 複素力学系 / Klein群 / 正則曲線 / 複素構造の変形 / マルチン核 / 調和関数 / ハウスドルフ次元 / リーマン面 / Martin境界 / モジュライ空間
Research Abstract

タイヒミュラー空間およびその境界が表現する平面領域の解析的性質について成果が得られた.たとえばタイヒミュラー空間の内部に現れる単連結領域がそのリーマン写像の増大度で特徴づけられた.このような領域は多次元空間でそのポテンシャル論的性質も研究され,新たな知見を得た.複素力学系では中立不動点の摂動において,放物的くりこみの概念が定義され,それを用いて局所不変集合の構造が決定された.多変数値分布論においては,準アーベル多様体での第二主要定理が証明され,正則曲線の代数的退化に対して新しい知見を得た.

Report

(5 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (148 results)

All 2009 2008 2007 2006 2005 2004 Other

All Journal Article (75 results) (of which Peer Reviewed: 61 results) Presentation (67 results) Book (6 results)

  • [Journal Article] Analytic construction of versal deformation of resolution of normal isolated singularities2009

    • Author(s)
      K. Miyajima
    • Journal Title

      J. Korean Math. Soc. 46,No.1

      Pages: 125-150

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Exponential Thurston maps and limit of quadratic differentials2009

    • Author(s)
      J. Hubbard, D. Schleicher, M. Shishikura
    • Journal Title

      J. Amer. Math. Soc. 22

      Pages: 77-117

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Riemann mappings of invariant components of Kleinian groups2009

    • Author(s)
      Shiga, H
    • Journal Title

      J.London Math.Soc. 90

      Pages: 716-728

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hypergeometric functions and hyperbolic metric2009

    • Author(s)
      G.D.Anderson, T.Sugawa, M.K Vamanamurthy, M.Vuorinen
    • Journal Title

      Comput.Methods Funct.Theory 9

      Pages: 269-284

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A coefficient inequality for Bloch functions with applications to uniformly locally univalent functions2009

    • Author(s)
      T.Sugawa, T.Terada
    • Journal Title

      Monatsh.Math. 156

      Pages: 167-173

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Uniformly locally univalent functions and Hardy spaces2009

    • Author(s)
      Y.C.Kim T.Sugawa
    • Journal Title

      J.Math.Anal.Appl. 353

      Pages: 61-67

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Equivalence between the boundary Harnack principle and the Carleson estimate2008

    • Author(s)
      H. Aikawa
    • Journal Title

      Math. Scad. 103,1

      Pages: 61-76

    • NAID

      120006459465

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Doubling conditions for harmonic measure in John domains2008

    • Author(s)
      H. Aikawa, K. Hirata
    • Journal Title

      Ann. Inst. Fourier 58,2

      Pages: 429-445

    • NAID

      120006459500

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] The second main theorem for holomorphic curves into semi-abelian varieties II2008

    • Author(s)
      Noguchi, J., Winkelmann, J., Yamanoi, K.
    • Journal Title

      Forum Math 20

      Pages: 469-503

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On multipliy connected wandering domains of entire functions2008

    • Author(s)
      M. Kisaka, M. Shishikura
    • Journal Title

      Cambridge Univ. Press 348

      Pages: 217-250

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Analytic families of holomorphic iterated function systems2008

    • Author(s)
      M. Roy, H. Sumi, M. Urbanski
    • Journal Title

      Nonlinearity 21

      Pages: 2255-2279

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Doubling conditions for harmonic measure in John domains2008

    • Author(s)
      H.Aikawa, K.Hirata
    • Journal Title

      Ann.Inst.Fourier(Grenoble) 58

      Pages: 429-445

    • NAID

      120006459500

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Equivalence between the boundary Harnack principle and the Carleson estimate2008

    • Author(s)
      H.Aikawa
    • Journal Title

      Math.Scad. 103

      Pages: 61-76

    • NAID

      120006459465

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A note on a theorem of Chuaqui and Gevirtz2008

    • Author(s)
      Y.C.Kim, T.Sugawa
    • Journal Title

      Ann.Acad.Sci.Fenn.Math. 33

      Pages: 273-279

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The limiting shape of one-dimensional Teichmuller spaces2008

    • Author(s)
      T.Sugawa
    • Journal Title

      Proc.Amer.Math.Soc. 136

      Pages: 2849-2858

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Norm estimates and univalence criteria for meromorphic functions2008

    • Author(s)
      S.Ponnusamy, T.Sugawa
    • Journal Title

      J.Korean Math.Soc. 45

      Pages: 269-284

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Denjoy-Wolff theorem on Riemann surfaces2008

    • Author(s)
      Hiroshige Shiga
    • Journal Title

      to appear in the Proceedings of the "International Workshop of Teichmuller theory and Moduli Problems" (掲載決定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Doubling conditions for harmonic measure in john domains2008

    • Author(s)
      H. Aikawa and K. Hirata
    • Journal Title

      Ann. Inst. Fourier 58no.1

      Pages: 429-445

    • NAID

      120006459500

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A construction of holomorphic families of Riemann surfaces over the punctured disk with given monodromy2008

    • Author(s)
      Y. Imayoshi
    • Journal Title

      to appear in Handbook of Teichmuller Spaces, The European Mathematical Society Vol.2(掲載決定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Topologcial Characterization of Postsingularly Finite Exponential Maps and Limits of Quadratic Differentials2008

    • Author(s)
      J. H. Hubbard, D. Schleicher and M. Shishikura
    • Journal Title

      Journal of Amer. Math. Soc. to appear (掲載決定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Boundary Harnack principle for p-harmonic functions in smooth Euclidean domains2007

    • Author(s)
      H. Aikawa, T. Kilpelainen, N. Shanmugalingam, X. Zhong
    • Journal Title

      Potential Anal. 26,3

      Pages: 281-301

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Integral representations of nonnegative solutions for parabolic equations and elliptic Martin boundaries2007

    • Author(s)
      Minoru Murata
    • Journal Title

      J. Func. Anal. 245

      Pages: 177-212

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Degeneracy of holomorphic curves into algebraic varieties2007

    • Author(s)
      Noguchi, J., Winkelmann, J., Yamanoi, K.
    • Journal Title

      J. Math. Pures Appl 88Issue3

      Pages: 293-306

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Some results in the analogue of Nevanlinna theory and Diophantine approximations2007

    • Author(s)
      Noguchi, J.
    • Journal Title

      Proc. Diophantine Geometry ed. U. Zannier

      Pages: 259-275

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Analytic approach to deformation of normal isolated singularities2007

    • Author(s)
      K. Miyajima
    • Journal Title

      World Scientific

      Pages: 279-289

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A construction of holomorphic families of Riemann surfaces over the punctured disk with given monodromy2007

    • Author(s)
      Y. Imayoshi
    • Journal Title

      Handbook of Teichmuller spaces, European Math. Soc. 2

      Pages: 101-108

    • Related Report
      2008 Final Research Report
  • [Journal Article] Degeneracy of holomorphic curves into algebraic varieties2007

    • Author(s)
      J. Noguchi, Winkelmann, J. and Yamanoi, K
    • Journal Title

      J. Math. Pures Appl 88 Issue3

      Pages: 293-306

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some results in the analogue of Nevanlinna theory and Diophantine approximations2007

    • Author(s)
      J. Noguchi
    • Journal Title

      Proc. Diophantine Geometry Ed. U. Zannier, Scoula Normal Superiore Pisa

      Pages: 259-275

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Analytic approach to deformation of normal isolated singularities2007

    • Author(s)
      K. Miyajima
    • Journal Title

      Real and Complex Singularities, Ed. L. Paunescu et. al. ゛World Scientific.

      Pages: 279-289

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Integral representations of nonnegative solutions for parabolic equations and elliptic Martin boundaries2007

    • Author(s)
      M. Murata
    • Journal Title

      J. Func. Anal 245

      Pages: 177-212

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Boundary Harnack principle for p-harmonic functions in smooth Euclidean domains,2007

    • Author(s)
      H. Aikawa, et. al.
    • Journal Title

      Potential Analysis 26

      Pages: 281-301

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Quasiconformal mapping class groups having common fixed points on the asymptotic Teichmuller spaces2007

    • Author(s)
      K. Matsuzaki
    • Journal Title

      J, d' Analyse Math 102

      Pages: 1-28

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Invariant differential operators associated with a conformal metric2007

    • Author(s)
      Seong-A Kim and T. Sugawa
    • Journal Title

      Michigan Math. J 55

      Pages: 459-479

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A general approach to the Fekete-Szego problem2007

    • Author(s)
      J. -H. Choi and Y. -C. Kim, and T. Sugawa
    • Journal Title

      J. Math. Soc. Japan 59

      Pages: 707-727

    • NAID

      10019539942

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Random dynamics of polynomials and devil's-staircase-like functions in the complex plane2007

    • Author(s)
      H. Sumi
    • Journal Title

      Appl. Math. Comput 187no.1

      Pages: 489-500

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The second main theorem for holomorphic curves into semi-abelian varieties II2007

    • Author(s)
      J.Noguchi, J.Winkelmann, K.Yamanoi
    • Journal Title

      Forum Math. (to appear)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Equivalence between the boundary Harnack principle and the Carleson estimate2007

    • Author(s)
      H.Aikawa
    • Journal Title

      Math. Scand. (to appear)

    • NAID

      120006459465

    • Related Report
      2006 Annual Research Report
  • [Journal Article] The interior of discrete projective structures in the Bers fiber2007

    • Author(s)
      K.Matsuzaki
    • Journal Title

      Ann. Acad. Sci. Fenn. 32

      Pages: 3-12

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Martin boundary points of a John domain and unions of convex sets2006

    • Author(s)
      H. Aikawa, K. Hirata, T. Lundh
    • Journal Title

      J. Math. Soc. Japan 58,1

      Pages: 247-274

    • NAID

      10017178462

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Holder estimates of p-harmonic extension operators2006

    • Author(s)
      H. Aikawa, N. Shanmugalingam
    • Journal Title

      J. Differential Equations 220,1

      Pages: 18-45

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotics of Green functions and the limiting absorption principle for elliptic operators with periodic coefficients2006

    • Author(s)
      Minoru Murata, (with Tetsuo Tsuchida)
    • Journal Title

      J. Math. Kyoto Univ. 46

      Pages: 713-754

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Representations of nonnegative solutions for parabolic equations2006

    • Author(s)
      Minoru Murata
    • Journal Title

      Advanced Studies in Pure Mathematics 44

      Pages: 283-289

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Deformation of complex structure on normal isolated singularities2006

    • Author(s)
      K. Miyajima
    • Journal Title

      Kyushu J. Math. 60

      Pages: 415-437

    • NAID

      130000063149

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A remark on holomorphic sections of certain holomorphic families of Riemann surfaces2006

    • Author(s)
      Y. Imayoshi, T. Nogi
    • Journal Title

      Proceedings of the 13th International Conference on Finite or Infinite Dimensional Complex Analysis and Application

      Pages: 101-108

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Semi-hyperbolic fibered rational maps and rational semigroups2006

    • Author(s)
      H. Sumi
    • Journal Title

      Ergodic Theory and Dynamical Systems 26

      Pages: 893-922

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Representations of nonnegative solutions for parabolic equations2006

    • Author(s)
      M.Murata
    • Journal Title

      Advanced Studies in Pure Mathematics 44

      Pages: 283-289

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Deformation of complex structure on normal isolated singularities2006

    • Author(s)
      K.Miyajima
    • Journal Title

      Kyushu Journal of Mathematics 60

      Pages: 415-437

    • NAID

      130000063149

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Semi-hyperbolic fibered rational maps and rational semigroups2006

    • Author(s)
      H.Sumi
    • Journal Title

      Ergodic Theory and Dynamical Systems 26

      Pages: 893-922

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Deformation of complex structure on normal isolated singularities2006

    • Author(s)
      Kimio Miyajima
    • Journal Title

      Kyushu J.Math 60(to appear)

    • NAID

      130000063149

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On complex analytic properties of limit sets and Julia sets2005

    • Author(s)
      Shiga, H.
    • Journal Title

      Kodai Math. J. 28

      Pages: 368-381

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the hyperbolic length and quasiconformal mappings2005

    • Author(s)
      Shiga, H.
    • Journal Title

      Complex Variables 50

      Pages: 123-130

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Uniqueness theorems for parabolic equations and Martin boundaries for elliptic equations in skew product form2005

    • Author(s)
      Minoru Murata
    • Journal Title

      J. Math. Soc. Japan 57

      Pages: 1-27

    • NAID

      10016419921

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A note on entire pseudo-holomorphic curves and the proof of Cartan-Nochka's theorem2005

    • Author(s)
      Noguchi, J.
    • Journal Title

      Kodai Math. J. 28

      Pages: 336-346

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Minori A remark on universal coverings of holomorphic families of Riemann surfaces2005

    • Author(s)
      Imayoshi, Yoichi, Nishimura
    • Journal Title

      Kodai Math. J. 28,no.2

      Pages: 230-247

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A construction of holomorphic families of Riemann surfaces over the punctured disk with given monodromy2005

    • Author(s)
      Imayoshi, Yoichi
    • Journal Title

      Finite or infinite dimensional complex analysis and applications

      Pages: 97-104

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Dimensions of Julia sets of expanding rational semigroups2005

    • Author(s)
      H. Sumi
    • Journal Title

      Kodai Math. J. Vol.28,No.2

      Pages: 390-422

    • NAID

      130003574500

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the hyperbolic length and quasiconformal mappings2005

    • Author(s)
      Hiroshige Shiga
    • Journal Title

      Complex Variables Theory App. 50

      Pages: 123-130

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Nevanlinna theory and Diophatine approximation2005

    • Author(s)
      J.Noguchi
    • Journal Title

      Proc.Conference on Several Complex Variabels, Beijin 2004, Sci. China Ser. A Math. 48

      Pages: 146-155

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A remark on holomorphic families of Riemann surfaces and their universal coverings spaces2005

    • Author(s)
      Yoichi Imayoshi, Minori Nishimura
    • Journal Title

      Kodai Mathematical Journal 28-2

      Pages: 230-247

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A countable Teichmuller modular group2005

    • Author(s)
      Katsuhik Matsuzaki
    • Journal Title

      Trans.Amer.Math.Soc. 357

      Pages: 3119-3131

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Dimensions of Julia sets of expanding rational semigroups2005

    • Author(s)
      Hiroki Sumi
    • Journal Title

      Kodai Mathematical Journal 28-2

      Pages: 390-422

    • NAID

      130003574500

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Linearity of the exceptional set for maps of P_k(C)2004

    • Author(s)
      J.-Y. Briend, S. Cantat, M. Shishikura
    • Journal Title

      Math. Ann. 330,no.1

      Pages: 39-43

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On some geometric properties of Teichmuller space

    • Author(s)
      L. Liu, H. Shiga, Z. Sun, H. Wei
    • Journal Title

      to appear in RIMS Kokyuroku Bessatsu "Infinite dimensional Teichmuller space and moduli space

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Modulus of continuity, a Hardy-Littlewood theorem and its application

    • Author(s)
      Shiga, H.
    • Journal Title

      to appear in RIMS Kokyuroku Bessatsu "Infinite dimensional Teichmuller space and moduli space

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Denjoy-Wolff theorem on Riemann surfaces

    • Author(s)
      Shiga, H.
    • Journal Title

      to appear in the Proceedings of the "International Workshop of Teichmuller theory and Moduli Problems

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Symmetric groups that are not the symmetric conjugates of Fuchsian groups

    • Author(s)
      K. Matsuzaki
    • Journal Title

      The proceedings of the Ahlfors-Bers colloquium, V, Contemporary Math., American Mathematical Society (to appear)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Structure theorem for holomorphic self-covers and its applications

    • Author(s)
      E. Fujikawa, K. Matsuzaki, M. Taniguchi
    • Journal Title

      Infinite dimensional Teichmuller space and moduli space, RIMS Kokyuroku Bessatsu, Research Institute of Mathematical Sciences, Kyoto Univ. (to appear)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On quasiconformal invariance of convergence and divergence types for Fuchsian groups

    • Author(s)
      K. Matsuzaki
    • Journal Title

      Illinois J. Math. (to appear)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Patterson-Sullivan measure and proper conjugation for Kleinian groups of divergence type, Ergodic Theory Dynam

    • Author(s)
      K. Matsuzaki, Y. Yabuki
    • Journal Title

      Systems (to appear)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] The connectivity of the Julia set and fixed points

    • Author(s)
      M. Shishikura
    • Journal Title

      Complex dynamics: families and friends

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Dynamics of polynomial semigroups with bounded postcritical set in the plane

    • Author(s)
      H. Sumi
    • Journal Title

      数理解析研究所講究録 1447

      Pages: 198-215

    • Related Report
      2008 Final Research Report
  • [Journal Article] Denjoy-Wolff theorem on Riemann surfaces

    • Author(s)
      Shiga, H
    • Journal Title

      Proceedings of the "International Workshop of Teichmuller theory and Moduli Problems" (掲載決定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Modulus of continuity, a Hardy-Littlewood theorem and its application

    • Author(s)
      Shiga, H
    • Journal Title

      "Infinite dimensional Teichmuller space and moduli space"(RIMS Kokyuroku Bessatsu) (掲載決定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On some geometric properties of Teichmuller space

    • Author(s)
      L.Liu, H.Shiga, Z.Sun, H.Wei
    • Journal Title

      "Infinite dimensional Teichmuller space and moduli space"(RIMS Kokyuroku Bessatsu) (掲載決定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Extensions of holomorphic motions and holomorphic families of isomorphisms of Mobius groups

    • Author(s)
      S.Mitra, H.Shiga
    • Journal Title

      to appear in Osaka J.Math (掲載決定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] 複雑領域上の正調和関数2009

    • Author(s)
      相川弘明
    • Organizer
      日本数学会(企画特別講演)
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-29
    • Related Report
      2008 Annual Research Report
  • [Presentation] Structure of nonnegative solutions for parabolic equations and perturbation theory for elliptic operators2009

    • Author(s)
      Minoru Murata
    • Organizer
      ソボレフ不等式とその周辺
    • Place of Presentation
      東北大学
    • Year and Date
      2009-03-23
    • Related Report
      2008 Final Research Report
  • [Presentation] Renormalizations in complex dynamics and the Teichmuller theory2009

    • Author(s)
      M. Shishikura
    • Organizer
      A Conference in Teichmuller Theory and Related Topics
    • Place of Presentation
      Graduate Center of CUNY, New York, USA
    • Year and Date
      2009-03-21
    • Related Report
      2008 Final Research Report
  • [Presentation] Monodromy and Complex Structures of Surface Fibrations Complex Analysis and Dynamics Seminar 2009/03/132009

    • Author(s)
      SHIGA HIROSHIGE
    • Organizer
      Graduate Center of CUNY Teichmuller Theory
    • Place of Presentation
      Here and there Colloquium City University, Queens college
    • Year and Date
      2009-03-16
    • Related Report
      2008 Final Research Report
  • [Presentation] Teichmuller Theory2009

    • Author(s)
      Shiga, H.
    • Organizer
      Here and there Colloquium
    • Place of Presentation
      Queens college
    • Year and Date
      2009-03-16
    • Related Report
      2008 Annual Research Report
  • [Presentation] Teichmuller Theory2009

    • Author(s)
      Shiga, H
    • Organizer
      Monodromy and Complex Structures of Surface Fibrations Complex Analysis and Dynamics Seminar
    • Place of Presentation
      Graduate Center of CUNY.
    • Year and Date
      2009-03-13
    • Related Report
      2008 Annual Research Report
  • [Presentation] Boundary Harnack principle and the quasihyperbolic boundary condition2009

    • Author(s)
      相川弘明
    • Organizer
      共同研究集会 Potential Theory and related Fields
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-02-18
    • Related Report
      2008 Annual Research Report
  • [Presentation] Structure of nonnegative solutions for parabolic equations and perturbation theory for elliptic operators2009

    • Author(s)
      Minoru Murata
    • Organizer
      Potential Theory and Related Fields
    • Place of Presentation
      数理解析研究所
    • Year and Date
      2009-02-17
    • Related Report
      2008 Final Research Report
  • [Presentation] Klein群と等角写像複素解析の発展とその応用2009

    • Author(s)
      志賀啓成
    • Place of Presentation
      桐生市民会館
    • Year and Date
      2009-01-25
    • Related Report
      2008 Final Research Report
  • [Presentation] Klein 群と等角写像2009

    • Author(s)
      Shiga, H
    • Organizer
      研究集会「複素解析の発展とその応用」
    • Place of Presentation
      桐生市民会館
    • Year and Date
      2009-01-25
    • Related Report
      2008 Annual Research Report
  • [Presentation] 力学系の研究に現れる複素解析的手法2009

    • Author(s)
      宍倉光広
    • Organizer
      複素解析の発展とその応用
    • Place of Presentation
      桐生
    • Year and Date
      2009-01-24
    • Related Report
      2008 Final Research Report
  • [Presentation] Extensions of holomorphic motions and holomorphic families of Mobius groups2009

    • Author(s)
      Shiga, H
    • Organizer
      研究集会「リーマン面・不連続群論」
    • Place of Presentation
      大阪大学理学部
    • Year and Date
      2009-01-11
    • Related Report
      2008 Annual Research Report
  • [Presentation] クライン群の正規部分群の収束指数の評価2009

    • Author(s)
      松崎克彦
    • Organizer
      リーマン面・不連続群論研究集
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-01-10
    • Related Report
      2008 Final Research Report
  • [Presentation] 正則写像の無理的中立不動点の不変集合2009

    • Author(s)
      宍倉光広
    • Organizer
      力学系研究集会
    • Place of Presentation
      軽井沢
    • Year and Date
      2009-01-10
    • Related Report
      2008 Final Research Report
  • [Presentation] Random complex dynamics and singular functions on the complex plane2009

    • Author(s)
      H. Sumi
    • Organizer
      UK-Japan Winter School Dynamics and Complexity
    • Place of Presentation
      University of Bath
    • Year and Date
      2009-01-08
    • Related Report
      2008 Final Research Report
  • [Presentation] 複雑領域上の正調和関数2009

    • Author(s)
      相川弘明
    • Organizer
      日本数学会
    • Place of Presentation
      東京大学
    • Related Report
      2008 Final Research Report
  • [Presentation] Boundary Harnack principle and the quasihyperbolic boundary condition2009

    • Author(s)
      相川弘明
    • Organizer
      京都大学数理解析研究所・共同研究集会
    • Related Report
      2008 Final Research Report
  • [Presentation] Beurling's minimum principle and the minimal thinness2009

    • Author(s)
      相川弘明
    • Organizer
      複素解析の発展とその応用
    • Place of Presentation
      桐生市市民文化センター
    • Related Report
      2008 Annual Research Report 2008 Final Research Report
  • [Presentation] Continuity problem of the extremal length2008

    • Author(s)
      相川弘明
    • Organizer
      International Workshop on Potential Theory 2008
    • Place of Presentation
      Gakushuin University
    • Year and Date
      2008-12-17
    • Related Report
      2008 Annual Research Report
  • [Presentation] The space of postcritically bounded 2-generator polynomial semigroups with hyperbolicity2008

    • Author(s)
      角大輝
    • Organizer
      Moduli and invariants in complex analysis and algebraic geometry
    • Year and Date
      2008-11-27
    • Related Report
      2008 Final Research Report
  • [Presentation] Some second main theorems and applications2008

    • Author(s)
      Noguch, J.
    • Organizer
      Workshop on Complex Hyperbolic Geometry and Related Topics, Fields Institute
    • Place of Presentation
      Canada
    • Year and Date
      2008-11-17
    • Related Report
      2008 Final Research Report
  • [Presentation] 接続と正則曲線のロンスキアンと第二主要定理について, 葉層の微分幾何とベルグマン核2008

    • Author(s)
      野口潤次郎
    • Organizer
      京都大学数理解析研究所研究集会
    • Year and Date
      2008-11-16
    • Related Report
      2008 Final Research Report
  • [Presentation] Unicity, Kobayashi hyperbolicity, rational points and examples2008

    • Author(s)
      Noguch, J.
    • Organizer
      Workshop on arithmetic and hyperbolic geometry, University of Montreal
    • Place of Presentation
      Canada
    • Year and Date
      2008-11-08
    • Related Report
      2008 Final Research Report
  • [Presentation] Semismall perturbations, semi-intrinsic ultracontractivity, and integral representations of nonnegative solutions for parabolic equations2008

    • Author(s)
      Minoru Murata
    • Organizer
      for parabolic equations, ポテンシャル論研究集会
    • Place of Presentation
      秋田市カレッジプラザ
    • Year and Date
      2008-11-02
    • Related Report
      2008 Final Research Report
  • [Presentation] Renormalization for irrationally indifferent fixed points of holomorphic functions2008

    • Author(s)
      M. Shishikura
    • Organizer
      Workshop on Complex Dynamics and Related Topics
    • Place of Presentation
      Fudan University, Shanghai, P.R. China
    • Year and Date
      2008-11-02
    • Related Report
      2008 Final Research Report
  • [Presentation] Random complex dynamics and singular functions on the complex plane2008

    • Author(s)
      H. Sumi
    • Organizer
      Complex dynamics and related topics
    • Place of Presentation
      Fudan University
    • Year and Date
      2008-11-01
    • Related Report
      2008 Final Research Report
  • [Presentation] Modulus of continuity に関する Hardy-Litlewood 型の定理とその応用2008

    • Author(s)
      Shiga, H
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-24
    • Related Report
      2008 Annual Research Report
  • [Presentation] Martin 境界, 塊界 Harnack 原理と擬双曲距離2008

    • Author(s)
      相川弘明
    • Organizer
      第55回幾何学論シンポジウム
    • Place of Presentation
      弘前大学
    • Year and Date
      2008-08-25
    • Related Report
      2008 Annual Research Report
  • [Presentation] Modulus of continuity2008

    • Author(s)
      SHIGA HIROSHIGE
    • Organizer
      a Hardy-Littlewood theorem and its application The 16th ICFIAA
    • Place of Presentation
      Dongguk University, Gyeongju, Korea
    • Year and Date
      2008-07-29
    • Related Report
      2008 Final Research Report
  • [Presentation] Modulus of continuity, a Hardy-Littlewood theorem and its application2008

    • Author(s)
      Shiga, H
    • Organizer
      The 16th ICFIAA
    • Place of Presentation
      Dongguk University, Gyeongju, Korea
    • Year and Date
      2008-07-29
    • Related Report
      2008 Annual Research Report
  • [Presentation] Some open problems in the value distribution theory and Kobayashi hyperbolic manifolds2008

    • Author(s)
      Noguch, J.
    • Organizer
      Hayama Symposium on Complex Analysis in Several Variables 2008
    • Place of Presentation
      Shonan Village Center
    • Year and Date
      2008-07-15
    • Related Report
      2008 Final Research Report
  • [Presentation] Random complex dynamics and singular functions on the complex plane2008

    • Author(s)
      H. Sumi
    • Organizer
      Aspects of Transcendental Dynamics
    • Place of Presentation
      Jacobs University Bremen
    • Year and Date
      2008-06-18
    • Related Report
      2008 Final Research Report
  • [Presentation] Families of Riemann Surfaces and Branched Coverings2008

    • Author(s)
      志賀啓成
    • Organizer
      数体および関数体上のディオファントス幾何
    • Place of Presentation
      国民宿舎紀伊見荘
    • Year and Date
      2008-02-22
    • Related Report
      2007 Annual Research Report
  • [Presentation] Structure of nonnegative solutions for parabolic equations and perturbation theory for elliptic operators2008

    • Author(s)
      Minoru Murata
    • Organizer
      マルコフ過程とデリクレ形式に関する話題
    • Place of Presentation
      熊本大学
    • Year and Date
      2008-02-17
    • Related Report
      2008 Final Research Report
  • [Presentation] Structure of nonnegative solutions for parabolic equations and perturbation theory for elliptic operators2008

    • Author(s)
      村田實
    • Organizer
      研究集会「マルコフ過程とデリクレ形式に関する話題」
    • Place of Presentation
      熊本大学
    • Year and Date
      2008-02-17
    • Related Report
      2007 Annual Research Report
  • [Presentation] Beurling's minimum principle and the minimal thinness2008

    • Author(s)
      相川弘明
    • Organizer
      ポテンシャル論研究集会
    • Place of Presentation
      秋田大学カレッジプラザ
    • Related Report
      2008 Annual Research Report 2008 Final Research Report
  • [Presentation] Recurrent orbits on L∞spaces2008

    • Author(s)
      K. Matsuzaki
    • Organizer
      Dynamics n' Analysis Seminar
    • Place of Presentation
      Wesleyan University, USA
    • Related Report
      2008 Final Research Report
  • [Presentation] General topology of moduli spaces of topologically infinite Riemann surfaces2008

    • Author(s)
      K. Matsuzaki
    • Organizer
      Colloquium of Math.
    • Place of Presentation
      Wesleyan University, USA
    • Related Report
      2008 Final Research Report
  • [Presentation] Symmetric groups that are not the symmetric conjugates of Fuchsian groups2008

    • Author(s)
      K. Matsuzaki
    • Organizer
      Geometric Function Theory and Geometry, 2008 Fall Eastern Section Meeting
    • Place of Presentation
      Wesleyan University, USA
    • Related Report
      2008 Final Research Report
  • [Presentation] 正規孤立特異点の特異点解消完備変形空間の解析的構成2007

    • Author(s)
      宮嶋公夫
    • Organizer
      平成19年度多変数関数論冬セミナー
    • Place of Presentation
      富山大学理学部
    • Year and Date
      2007-12-23
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] On conformal mappings and Kleinian groups2007

    • Author(s)
      志賀啓成
    • Organizer
      等角写像論・値分布論合同研究集会
    • Place of Presentation
      慶応大学理工学部
    • Year and Date
      2007-12-08
    • Related Report
      2007 Annual Research Report
  • [Presentation] ランダムな複素力学系、有理半群と複素平面上の特異関数2007

    • Author(s)
      角大輝
    • Organizer
      研究集会「力学系と微分方程式」
    • Place of Presentation
      広島大学
    • Year and Date
      2007-11-09
    • Related Report
      2007 Annual Research Report
  • [Presentation] 摂動論と放物型方程式の非負値解2007

    • Author(s)
      村田實
    • Organizer
      研究集会「微分方程式と数理物理」
    • Place of Presentation
      ウエルハートピア萩
    • Year and Date
      2007-11-05
    • Related Report
      2007 Annual Research Report
  • [Presentation] On the degeneracy of holomorphic curves2007

    • Author(s)
      野口潤次郎
    • Organizer
      Complex Geometxy in Osaka
    • Place of Presentation
      Japan
    • Year and Date
      2007-11-02
    • Related Report
      2007 Annual Research Report
  • [Presentation] On conformal mappings and Kleinian groups無限次元タイヒミュラー空間とモジュライ空間2007

    • Author(s)
      SHIGA HIROSHIGE
    • Place of Presentation
      数理解析研究所
    • Year and Date
      2007-11-01
    • Related Report
      2008 Final Research Report
  • [Presentation] フラクタルな境界を持つ領域の等角写像について確率論とPDE2007

    • Author(s)
      志賀啓成
    • Place of Presentation
      広島大学学士会館
    • Year and Date
      2007-10-15
    • Related Report
      2008 Final Research Report
  • [Presentation] フラクタルな境界を持つ領域の等角写像について2007

    • Author(s)
      志賀啓成
    • Organizer
      確率論とPDE
    • Place of Presentation
      広島大学学士会館
    • Year and Date
      2007-10-15
    • Related Report
      2007 Annual Research Report
  • [Presentation] 円周上の群不変対称構造のタイヒミュラー空間2007

    • Author(s)
      松崎克彦
    • Organizer
      函数論シンポジウム
    • Place of Presentation
      群馬県桐生市
    • Year and Date
      2007-10-08
    • Related Report
      2007 Annual Research Report
  • [Presentation] 半一様領域と調和測度のダブリング性について2007

    • Author(s)
      相川弘明
    • Organizer
      第50回函数論シンポジウム
    • Place of Presentation
      群馬県桐生市
    • Year and Date
      2007-10-07
    • Related Report
      2007 Annual Research Report
  • [Presentation] Deformation of CR structure on a boundary of isolated singularities2007

    • Author(s)
      K. Miyajima
    • Organizer
      Conference in complex analysis and geometry
    • Place of Presentation
      CIRM, Marseille, France
    • Year and Date
      2007-09-26
    • Related Report
      2008 Final Research Report
  • [Presentation] Conference in complex analysis and geometry2007

    • Author(s)
      K.MIYAJIMA
    • Organizer
      Deformation of CR structure on a boundary of isolated singularities
    • Place of Presentation
      CIRM, Marseille, France
    • Year and Date
      2007-09-26
    • Related Report
      2007 Annual Research Report
  • [Presentation] Uniformly perfect sets and Hardy spaces2007

    • Author(s)
      T. Sugawa
    • Organizer
      University of Helsinki, Finland
    • Place of Presentation
      Finland-Japan Joint Seminar on Analysis
    • Year and Date
      2007-08-28
    • Related Report
      2008 Final Research Report
  • [Presentation] Uniformly perfect sets and Hardy spaces2007

    • Author(s)
      須川敏幸
    • Organizer
      Finland-Japan Joint Seminar on Analysis
    • Place of Presentation
      University of Helsinki, Finland
    • Year and Date
      2007-08-28
    • Related Report
      2007 Annual Research Report
  • [Presentation] Value distribution and distribution of rational points2007

    • Author(s)
      野口潤次郎
    • Organizer
      Spectral Analysis in Geometry and Number Theory
    • Place of Presentation
      Nagoya
    • Year and Date
      2007-08-07
    • Related Report
      2007 Annual Research Report
  • [Presentation] Uniformly locally univalent functions and Hardy spaces2007

    • Author(s)
      T. Sugawa
    • Organizer
      15th ICFIDCAA
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2007-08-02
    • Related Report
      2008 Final Research Report
  • [Presentation] Classification of polynomial semigroups and random Julia sets that are Jordan curves but not quasicircles2007

    • Author(s)
      角大輝
    • Organizer
      15th International conference of finite and infinite dimensional complex analysis and applications
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2007-07-31
    • Related Report
      2007 Annual Research Report
  • [Presentation] On Bazilevic functions2007

    • Author(s)
      須川敏幸
    • Organizer
      幾何学的単葉関数論の研究
    • Place of Presentation
      数理解析研究所
    • Year and Date
      2007-05-17
    • Related Report
      2007 Annual Research Report
  • [Presentation] Uniqueness of the Patterson-Sullivan measure and proper conugation of Kleinian groups2007

    • Author(s)
      松崎克彦
    • Organizer
      Colloquium of Math. Department
    • Place of Presentation
      Wesleyan Univ., Connecticut, USA
    • Year and Date
      2007-05-01
    • Related Report
      2007 Annual Research Report
  • [Presentation] 強擬凸領域と特異点の変形, 微分幾何学セミナー2007

    • Author(s)
      宮嶋公夫
    • Place of Presentation
      筑波大学大学院物質理学研究科
    • Year and Date
      2007-02-19
    • Related Report
      2008 Final Research Report
  • [Presentation] 2次微分に付随するリーマン面上の計量について2007

    • Author(s)
      須川敏幸
    • Organizer
      リーマン面・不連続群論合同研究集会
    • Place of Presentation
      島根大学
    • Year and Date
      2007-02-02
    • Related Report
      2008 Final Research Report
  • [Presentation] Continuity problem of the extremal length2007

    • Author(s)
      H. Aikawa
    • Organizer
      International Workshop on Potential Theory 2008
    • Place of Presentation
      Tokyo-Mejiro, Gakushuin University
    • Related Report
      2008 Final Research Report
  • [Presentation] The rigidity of irrationally indifferent fixed points via Parabolic renormalization2007

    • Author(s)
      宍倉光広
    • Organizer
      Renormalization, small divisors, continued fractions and geodesic flows
    • Place of Presentation
      Ennio De Giorgi Mathematics Research Center of the Scuola Normale Superiore Pisa
    • Related Report
      2007 Annual Research Report
  • [Presentation] Renormalization in Complex Dynamics and iteration in a Teichmuller space2007

    • Author(s)
      宍倉光広
    • Organizer
      Hayama Symposium on Complex Analysis in Several Variables
    • Place of Presentation
      葉山
    • Related Report
      2007 Annual Research Report
  • [Presentation] Hausdorff moment problem and geometric function theory2006

    • Author(s)
      T. Sugawa
    • Organizer
      Finland-Japan Joint Seminar on Analysis
    • Place of Presentation
      広島大学
    • Year and Date
      2006-12-13
    • Related Report
      2008 Final Research Report
  • [Presentation] Hausdorff moment problem and polylogarithms2006

    • Author(s)
      T. Sugawa
    • Organizer
      角写像論・値分布論合同研究集会
    • Place of Presentation
      広島大学
    • Year and Date
      2006-12-03
    • Related Report
      2008 Final Research Report
  • [Presentation] An analytic approach to the Res-functor2006

    • Author(s)
      K. Miyajima
    • Organizer
      Mini-Symposium on ingularity theory, Algebraic geometry and Complex analysis
    • Place of Presentation
      鹿児島大学理学部
    • Year and Date
      2006-08-21
    • Related Report
      2008 Final Research Report
  • [Presentation] A construction of holomorphic families of Riemann surfaces over the punctured disk with given monodromy2005

    • Author(s)
      今吉洋一
    • Organizer
      リーマン面に関連する位相幾何学
    • Place of Presentation
      東京大学
    • Related Report
      2008 Final Research Report
  • [Book] 複雑領域上のディリクレ問題-ポテンシャル論の観点から2008

    • Author(s)
      相川弘明
    • Total Pages
      302
    • Publisher
      岩波書店
    • Related Report
      2008 Final Research Report
  • [Book] Boundary Harnack principle and the quasihyperbolic boundary condition, in Sobolev Spaces in Mathematics II2008

    • Author(s)
      H. Aikawa
    • Publisher
      Springer Verlag
    • Related Report
      2008 Final Research Report
  • [Book] Boundary Harnack principle and the quasihyperbolic boundary condition, in Sobolev Spaces in Mathematics II, Applications in Analysis and Partial Differential Equations2008

    • Author(s)
      相川弘明
    • Total Pages
      12
    • Publisher
      Springer Verlag
    • Related Report
      2008 Annual Research Report
  • [Book] 複雑領域上のディリクレ問題-ポテンシャル論の観点から(岩波数学叢書)2008

    • Author(s)
      相川弘明
    • Total Pages
      302
    • Publisher
      岩波書店
    • Related Report
      2008 Annual Research Report
  • [Book] 楕円型・放物型偏微分方程式2006

    • Author(s)
      村田實
    • Publisher
      岩波書店
    • Related Report
      2008 Final Research Report
  • [Book] Potential theory in Matsue, Advanced Studies in Pure Mathematics2004

    • Author(s)
      H. Aikawa, T. Kumagai, Y. Mizuta, N. Suzuki eds.
    • Total Pages
      413
    • Publisher
      Theory held at Shimane University
    • Related Report
      2008 Final Research Report

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Published: 2005-04-01   Modified: 2016-04-21  

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