複素解析構造の総合的研究

2002 Fiscal Year Annual Research Report

• Project/Area Number: 13304009
• Research Institution: The University of Tokyo
• Principal Investigator: 野口 潤次郎 東京大学, 大学院・数理科学研究科, 教授 (20033920)
• Co-Investigator(Kenkyū-buntansha): 満渕 俊樹 大阪大学, 大学院・理学研究科, 教授 (80116102) ; 大沢 健夫 名古屋大学, 大学院・多元数理科学研究科, 教授 (30115802) ; 藤本 坦孝 金沢大学, 理学部, 教授 (60023595) ; 宍倉 光広 京都大学, 大学院・理学研究科, 教授 (70192606) ; 風間 英明 九州大学, 大学院・数理学研究院, 教授 (10037252)
• Keywords: 多変数複素解析 / 幾何学的複素解析 / 小林双曲的多様体 / 値分布 / 擬凸領域 / モジュライ空間 / 複素力学系 / タイヒミューラー空間

Research Abstract

昨年度に開催された岡潔生誕百年記念多変数複素解析国際会議京都/奈良2001,で得られた成果を発表する準備をしている.そこで明らかになった諸問題を,各分担者を中心に研究が進められた.また今年度は,葉山多変数複素解析シンポジウムを開催し内外の多くの参加者を得,成果の国際的発信を行い,共同研究を行った.
代表者を中心として正則写像の値分布の研究が行われた.関数体上で準アーベル多様体のイロハ予想の類似を証明し有限性定理を得た.高次元小林双曲的射影超曲面で算術的有限性を持つものを構成した.また準アーベル多様体内の正則曲線のジェット像の構造定理を得た.山ノ井は,小関数の打ち切り個数関数を用いる第二主要定理の証明をした。藤本は,一意性多項式になる為の条件を完全に決定した.下村は,Painleve超越関数PIVについて,小関数に関する値分布を調べ,増大度の上からの評価を得ることに成功した.相原と森は共同で複素射影空間内の任意の超曲面に対して,その超曲面から定まる定数と0との間にある任意の実数を除外指数として持つ有理型写像を構成した。
大沢はL^2拡張定理を複素多様体上で証明した.清水と児玉は,非有界領域C^k×(C^*)^lの特徴付け行った.
宮嶋,赤堀らは,正規孤立特異点のモジュライに関して強擬凸CR構造の変形を通じての記述に成功した.平地は,CR幾何学および共形幾何学に現れるスカラー不変量の解析を行った.その結果,共形,CRの二つの枠組みでのQ-曲率はアンビエント計量を用いた同一の表示を持つことを示した.泊は,曲線特異点に対し多重種数δ_mを定義し、通常特異点の特徴づけを得た。
満渕は,定スカラー曲率射影代数多様体の漸近的安定性を示した.辻は,多重種数の変形不変性を劣随伴公式の形に一般化した。高山は,代数多様体上の正則直線束とその特異エルミート計量の組に対し、新しい交点理論を展開し、幾つかの基本的な結果を得た。
その他複素力学系,リーマン面のモジュライ理論,多変数正則関数空間,補間問題,ポテンシャル論での研究の進展をみた.

Research Products

• [Publications] J.Noguchi, J.Winkelmann: "Holomorphic curves and integral points off divisors"Math. Z.. 239. 593-610 (2002)
• [Publications] J.Noguchi, J.Winkelmann, K.Yamanoi: "The second main theorem for helomorphc curves into semi-Abelian varieties"Acta Math.. 188. 129-161 (2002)
• [Publications] J.Noguchi: "Geometric Diophantine Problems---有理点分布と値分布,「Communications in Arithmetic Fundamental Groups」"京都大学数理解析研究所講究録. 1267. 2-4 (2002)
• [Publications] J.Noguchi: "Some results in view of Nevanlinna theory"Number Theoretic Methods-Future Trends, China-Japan Seminar 2001. Acad Publ(To appear).
• [Publications] J.Noguchi: "An arithmetic property of Shirosaki's hyperbolic projective hypersurface"Forum Math.. (To appear).
• [Publications] 野口潤次郎: "ネヴァンリンナ理論とイロハ(abc-)予想"京都大学数理解析研究所講究録. (To appear).
• [Publications] J.Noguchi: "Intersection multiplicities of holomorphic and algebraic curves with divisors"Proc. OKA 100 Conference Kyoto/Nara 2001. (To appear).
• [Publications] Noguchi, J., Winkelmann, J.: "A note on jets of entire curves in semi-abelian varieties"Math. Z.. (To appear).
• [Publications] K.Fujita, M.Morimoto: "On the double series expansion of holomorphic functions"J. Math. Anal. Appl.. 272. 335-348 (2002)
• [Publications] K.Fujita, M.Morimoto: "Analytic functions and analytic functionals on some balls"Proceedings of the Third ISAAC Congress, Kluwer Academic Publishers. (To appear). (2002)
• [Publications] M.Morimoto, K.Fujita: "Holomorphic functions on the Lie ball and related topics"Proceedings of the ninth Finite or Infinite Dimensional Complex Analysis and Applications, Kluwer Academic Publisher. 33-44 (2002)
• [Publications] K.Fujita: "Bergman transformation for analytic functionals on some balls"Microlocal Analysis and Complex Fourier Analysis. 81-98 (2002)
• [Publications] S.Kamiya, J.R.Parker: "On discrete subgroups of PU(1,2 ; C) with Heisenberg translations II"Rev.Romaine Math. Pures Appl.. (To appear).
• [Publications] Y.Jiang, S.Kamiya, J.R.Parker: "Jorgensen's inequality for complex hyperbolic space"Geometriae Dedicata. (To appear).
• [Publications] S.Kamiya, J.R.Parker: "Notes on discrete subgroups of PU(1,2;C) with Heisenberg translations IV"京都大学数理解析研究所講究録. 1270. 138-144 (2002)
• [Publications] S.Izumi, S.Koike, T.-C.Kuo: "Computations and stability of Fukui invariant"Compositio Mathematica. 130. 49-73 (2002)
• [Publications] S.Izumi: "Flatness of differentiable functions along a subset of a real analytic set"Journal d'Analyse Mathematique. 86. 235-246 (2002)
• [Publications] S.Takayama: "Iitaka's fibrations via multiplier ideals"Trans. Amer. Math. Soc. 355. 37-47 (2003)
• [Publications] Masataka TOMARI: "Multiplicity of filtered rings and simple K3 singularities of multiplicity two"Publ. RIMS, Kyoto Univ.. 38. 693-724 (2002)
• [Publications] Masako Furuya, Masataka TOMARI: "A characterization of semi-quasihomogeneous function in terms of the Milnor number"Proc. Amer. Math. Soc.. (To appear).
• [Publications] M.Kato: "A Schwarz map of Appell's F_2 with projective monodromy group of order 25920"Kyushu J. Math.. (To appear).
• [Publications] M.Kato, M.Noumi: "Monodromy groups of hypergeometric functions satisfying algebraic equations"Tohoku Math. J.. (To appear).
• [Publications] Makoto Masumoto: "Algebraic relations among extremal lengths of homology classes on compact Riemann surfaces"Math. Nachr.. 239/240. 157-169 (2002)
• [Publications] Makoto Masumoto, Masakazu Shiba: "Hyperbolically maximal domains and fundamental domains for a discontinuous group of conformal automorphisms of a Riemann surface"Quart. J. Math. Oxford Ser. (2). 53. 337-346 (2002)
• [Publications] H.Tsuji: "Deformation Invariance of Plurigenra"Nagoya Math. J.. 166. 117-134 (2002)
• [Publications] G.Schumacher, H.Tsuji: "Quasiprojectivity of Moduli Spaces of Polarized Varieties"Annals of Mathematics. (To appear). (2003)
• [Publications] H.Tsuji: "Subadjunction Theorem"Proceedings of Oka 100. (To appear).
• [Publications] W.Bergweiler, K.Ishizaki, N.Yanagihara: "Growth of meromorphic solutions of some functional equations I"Aequationes Math.. 63. 140-151 (2002)
• [Publications] K.Ishizaki, I.Laine, S.Shimomura, K.Tohge: "Riccati differential equations with elliptic coefficients II"Tohoku Math. J.. (To appear).
• [Publications] K.Ishizaki: "A note on Factorization of the Weierstrass Pe-function"Proceedings of Third ISAAC Congress. (To appear).
• [Publications] K.Ishizaki: "A note on the functional equation f^h+g^n+h^n=1 and some complex differential equations"Computational Method and Functional Theory. (To appear).
• [Publications] T.Honda: "The growth theorem for k-fold symmetric convex mappings"Bulletin of the London Mathematical Society. 34. 717-724 (2002)
• [Publications] C.H.Chu, T.Honda: "A Schwarz lemma for bounded symmetric domains in Hilbert spaces"the Mathematical Proceedings of the Royal Irish Academy. (To appear).
• [Publications] M.Abe: "Meromorphic convexity of normality domains"Complex Analysis and Related Topics, Proceedings of the Japan-Korea Joint Workshop in Mathematics 2001, Yamaguchi, Japan, 22--24July 2001. 1-6 (2002)
• [Publications] M.Abe: "Steinness of the total space of a non-trivial algebraic affine C-bundle on the punctured complex affine plane"Mathematische Nachrichten. 238. 16-22 (2002)
• [Publications] M.Abe, T.Jin, T.Shima: "Remarks on universal functions of 0 C^*"Hiroshima Mathematical Journal. 33(To appear). (2003)
• [Publications] K.Sawada: "Picard constants of n-sheeted algebroid surfaces"Kodai Math. J.. 25 No.2. 113-138 (2002)
• [Publications] Y.Matsugu, S.Ueki: "Isometries of weighted Bergman-Privalov spaces on the unit ball of C^n"J. Math. Soc. Japan. 54. 341-347 (2002)
• [Publications] Y.Matsugu, J.Miyazawa, S.Ueki: "A characterization of weighted Bergman-Privalov spaces on the unit ball in C^n"J. Korean Math. Soc.. 39. 783-800 (2002)
• [Publications] (2)Y.Matsugu, J.Miyazawa: "A characterization of weighted Bergman-Orlicz spaces on the unit ball of C^n"J. Austral. Math. Soc.. 73. 1-13 (2002)
• [Publications] 木村秀幸: "位数p^3の非可換群の対称種数"愛知産業大学紀要. 10. 67-72 (2002)
• [Publications] 栗林泉, 木村秀幸: "A classification of automorphism groups up to topological equivalence of compact Riemann surface of genus 2"浜松大学経営情報学部紀要. 15. 115-123 (2002)
• [Publications] 木村秀幸: "閉リーマン面上の群作用が定める母関数"京都大学数理解析研究所講究録. 1270. 51-62 (2002)
• [Publications] S.Tajima: "Exponential polynomials and the Fourier-Borel transforms of algebraic local cohomology classes"Microlocal Analysis and Complex Fourier Analysis, eds by T.Kawai and K.Fujita, World Scientific Publishing. 284-296 (2002)
• [Publications] S.Tajima: "Inhomogeneous ordinaly differential equations, local cohomology and residues"Finite or infinite dimensional Complex Analysis, Hanoi. Kluwer(To appear).
• [Publications] Y.Nakamura, S.Tajima: "A method for constructing holonomic systems for algebraic local cohomology classes with support on a zero dimensional variety"Mathematical Software ICMS 2002, World Scientific. 158-168 (2002)
• [Publications] 田島慎一, 中村弥生: "代数的局所コホモロジー類の満たすホロノミック系の構成法についてII"京都大学数理解析研究所講究録. (To appear).
• [Publications] 田島慎一: "非同次常微分方程式の可解条件についてII"京都大学数理解析研究所講究録. (To appear).
• [Publications] 田島慎一: "Holonomicな定数係数線形偏微分方程式とGrothendieck duality"京都大学数理解析研究所講究録. (To appear).
• [Publications] S.Shimizu: "Prolongation of holomorphic vector fields on a tube domain and its applications"The Proceedings of the Memorial Conference of Kiyoshi Oka's Centennial Birthday on Complex Analysis in Several Variables, Kyoto/Nara 2001. (To appear).
• [Publications] F-Y.Maeda, T.Ono: "Perturbation theory for nonlinear Dirichlet problems"Ann. Acad. Sci. Fenn.. 28(To appear). (2003)
• [Publications] M.Nakai, T.Tada: "The role of continuum hypothesis in the theory of harmonic dimensions"Bull. Daido Inst. Tec.. 38(To appear). (2002)
• [Publications] D.Partyka, K.Sakan: "On Heinz's inequality"Bull. Soc. Sci. Lettres Lodz. (To appear). (2003)
• [Publications] Y.Abe: "Construction of automorphic forms for ample factors of quasi-abelian varieties"Kyushu J. Math.. 57(To appear). (2003)
• [Publications] Y.Abe, P.Zappa: "Universal functions on Stein manifolds"J. Math. Soc. Japan. 55(To appear). (2003)
• [Publications] W.Bergweiler, Shunsuke Morosawa: "Semihyperbolic entire functions"Nonlinearity. 15. 1673-1684 (2002)
• [Publications] K.Adachi: "L^p extension of holomorphic functions from submanifolds to strictly pseudoconvex domains with non-smooth boundary"Nagoya Mathematical Journal. (To appear).
• [Publications] K.Kasuga: "Correction to the paper : "There are no codimension 1 linear isometries on the ball and polydisk algebras"Sci. Math. Jpn.. 56. 69-70 (2002)
• [Publications] Shigeki Oh'uchi: "Interpolation on countably many algebraic subsets for weighted entire functions"Osaka Journal of Mathematics. 39. 97-121 (2002)
• [Publications] Shun Shimomura: "On deficiencies of small functions for Painleve transcendents of the fourth kind"Ann. Acad. Sci. Fenn. Ser. A I Math.. 27. 109-120 (2002)
• [Publications] Shun Shimomura: "Oscillation results for n-th order linear differential equations with meromorphic periodic coefficients"Nagoya Math. J.. 166. 55-82 (2002)
• [Publications] Shun Shimomura: "Growth of the first, the second and the fourth Painleve transcendents"Math. Proc. Camb. Phil. Soc.. (To appear).
• [Publications] Shun Shimomura: "Riccati differential equations with elliptic coefficients, II"Tohoku Math. J.. (To appear).
• [Publications] Shun Shimomura: "Lower estimates for the growth of Painleve transcendents"Funkcial. Ekvac.. (To appear).
• [Publications] Shun Shimomura: "Growth of modified Painleve transcendents of the fifth and the third kind"Forum Math.. (To appear).
• [Publications] G.G.Gundersen, K.Tohge: "Unique range sets for polynomials or rational functions"Proceedings of the 3rd ISAAC Congress. (To appear). (2003)
• [Publications] K.Ishizaki, I.Laine, S.Shimomura, K.Tohge: "Riccati differential equations with elliptic coefficients, II"Tohoku Mathematical Journal. (To appear). (2003)
• [Publications] H.Yoshida, I.Miyamoto: "Two criterions of Wiener type for minimally thin sets and rarefied sets in a cone"J. Math. Soc. Japan. 54. 488-512 (2002)
• [Publications] H.Yoshida, I.Miyamoto, M.Yanagishita: "Beuring-Dahlberg-Sjogren type theorems for minimally thin sets in a cone"Canad. Math. Bull.. (To appear).
• [Publications] K.Matsumoto: "On the cohomological completeness of q-complete domains with corners"Nagoya Math. J.. 168. 105-112 (2002)
• [Publications] K.Matsumoto, T.Ohsawa: "On the real analytic Levi flat hypersurfaces in complex tori of dimension two"Ann. Inst. Fourier(Grenoble). 52. 1525-1532 (2002)
• [Publications] K.Matsumoto: "Levi form of logarithmic distance to complex submanifolds and its application to developability"Adv. Stud. Pure Math.. (To appear).
• [Publications] Yoshihiro Aihara: "Algebraic dependence of merormorphic mappings in value distribution theory"Nagoya Math. J.. 169(To appear). (2003)
• [Publications] Yoshihiro Aihara: "Uniqueness problem for meromorphic mappings under conditions on the preimages of divisors"Proc. of the Memorial Conference of Kiyoshi Oka's Centennial Birthday on Complex Analysis in Several Variables, Kyoto/Nara 2001, in Advanced Studies in Pure Math.. (To appear).
• [Publications] H.Aikawa: "Holder continuity of the Dirichlet solution for a general domain"Bull. London Math. Soc.. 34. 691-702 (2002)
• [Publications] H.Aikawa, K.Hirata, T.Lund: "Martin boundary for union of convex sets"数理解析研究所講究録「ポテンシャル論とその周辺」. 1293. 1-14 (2002)
• [Publications] 相川弘明: "複雑領域のMartin境界と境界Harnack原理"数学. 55(To appear). (2003)
• [Publications] H.Aikawa, T.Lundh, T.Mizutani: "Martin boundary of a fractal domain"Potential Anal.. (To appear).
• [Publications] H.Aikawa: "Positive harmonic functions of finite order in a Denjoy type domain"Proc. Amer. Math. Soc.. (To appear).
• [Publications] A.Fujiki: "Topology of compact self-dual manifolds whose twistor space is of positive algebraic dimension"7. 587-608 (2002)
• [Publications] A.Fujiki: "Anti-holomorphic involutions of elliptic curves and a diffeomorphism type of certain self-dual manifolds"Lecture Note Series Math.. 7. 15-32 (2002)
• [Publications] A.Fujiki: "n the general fiber of an algebraic reduction of a compact complex manifolds of algebraic codimension two"J.Math. Kyoto Univ.. 42(To appear). (2002)
• [Publications] K.Yamanoi: "Algebro-geometric version of Nevanlinna's lemma on logarithmic derivatives and applications"Nagoya Math. J.. (To appear).
• [Publications] K.Yamanoi: "On Nevanlinna theory for holomorphic curves in Abelian varieties"Proceedings of the Memorial Conference of Kiyoshi Oka's Centennial Birthday on Complex Analysis in Several Variables, Kyoto/Nara 2001. (To appear).
• [Publications] M.Kobayashi: "Convergence of Invariant Distances on Decreasing Domains"Complex Variables Theory Appl.. 47. 155-165 (2002)
• [Publications] J.Kajiwara, X.D.Li, K.H.Shon: "Regeneration in Complex, Quaternionand Clifford Analysis"Finite or Infinite Dimensional Complex Analysis, Kluwer Academic Publisher(Dordrecht/Boston/London). (To appear). (2002)
• [Publications] J.Kajiwara, X.D.Li, K.H.Shon: "Regeneration in Quaternion Analysis"Indian Jousnal of Mathematics. (To appear). (2003)
• [Publications] 亀山弘, 岩井浩光, 服部晃, 竹内茂: "大学院数学教育を考える"岐阜大学教育学部研究報告(自然科学). 26-2. 1-18 (2002)
• [Publications] 竹内茂: "数学教育国際協力研究(2)アルゼンチン-その2"岐阜大学教育学部研究報告(自然科学). 27-1. 1-14 (2002)
• [Publications] Shigeru Takeuchi: "Math Ed and in/pre-service teacher training"Proc. of the ICM2002 Satellite International Conference on math education, Tibet University, Lhasa, China, August 12-17. (2002)
• [Publications] T.Mabuchi: "Multiplier Hermitian structures on Kahler manifolds"Nagoya Math. J.. (To appear).
• [Publications] A.Futaki, T.Mabuchi: "Moment maps and symmetric multilinear forms associated with symplectic classes"Asian Math. J.. 6. 349-372 (2002)
• [Publications] T.Mabuchi, Y.Nakagawa: "The Bando-Calabi-Futaki character as an obstruction to semistability"Math. Ann.. 324. 187-193 (2002)
• [Publications] T.Mabuchi: "Heat Kernel estimates and the Green functions on multiplier Hermitian manifolds"Tohoku Math. J.. 54. 259-275 (2002)
• [Publications] T.Mabuchi: "A theorem of Calabi-Matsushima's type"Osaka J. Math.. 39. 1-9 (2002)
• [Publications] H.Fujimoto: "On uniqueness polynomials for meromorphic functions"Nagoya Mathematical Journal. (To appear). (2003)
• [Publications] T.Umeno: "Period matrices for quasi-Abelian varieties"Japan. J. Math. 29(To appear). (2003)
• [Publications] T.Umeno: "On quasi-Abelian varieties over non-algebraic complex tori"Proceedings of the Sixth International Workshop on Real and Complex Analysis. (To appear). (2002)
• [Publications] 中川三留, 瀬川重男: "被覆面の型"数理解析研究所講究録. 1277. 84-93 (2002)
• [Publications] 吉永 悦男, 福井 敏純, 泉 脩藏: "特異点の数理3:解析関数と特異点"共立出版. 426 (2002)
• [Publications] V.I.Gromak, I.Laine, S.Shimomura: "Painleve Differential Equations in the Complex Plane"Walter de Gruyter. 303 (2002)
• [Publications] 相川弘明(編集): "ポテンシャル論とその周辺 講究録1293"京都大学数理解析研究所. 198 (2002)
• [Publications] 荷見守助, 下村勝孝: "線型代数入門"内田老鶴圃. 215 (2002)
• [Publications] Ohsawa, T.: "Analysis of several complex variables"Iwanami Series in Modern Mathematics. 211 (2002)