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Ideal boundary of covering surfaces

Research Project

Project/Area Number 14540192
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionKyoto Sangyo University

Principal Investigator

MASAOKA Hiroaki  Kyoto Sangyo University, Faculty of Science, Professor, 理学部, 教授 (30219315)

Co-Investigator(Kenkyū-buntansha) SEGAWA Shigeo  Daido Institute of Technology, School of Liberal Arts and Sciences, Professor, 教養部, 教授 (80105634)
TSUJI Mikio  Kyoto Sangyo University, Faculty of Science, Professor, 理学部, 教授 (40065876)
ISHIDA Hisashi  Kyoto Sangyo University, Faculty of Science, Professor, 理学部, 教授 (10103714)
JIN Naondo  Shiga University, Faculty of Education, Lecturer, 教育学部, 講師 (90206368)
NISHIO Masaharu  Osaka City University, Graduate school of Science, Associate professor, 大学院・理学研究科, 助教授 (90228156)
Project Period (FY) 2002 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2003: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2002: ¥1,400,000 (Direct Cost: ¥1,400,000)
Keywordsfinitely sheeted unlimited covering surface / Martin boundary / Kuramochi boundary / quasiconformal mapping / harmonic dimension / Denjoy domain / nonlinear second order hyperbolic equation / caloric morphism / Heins型被覆面 / 2階双曲型方程式 / ダンジョア領域 / 無限葉被覆面 / 熱方程式
Research Abstract

1.(1)For a Riemann surface Rand a finitely sheeted unlimited covering surface W of R, by Martin boundaries (resp. Kuramochi boundaries) of Rand W Masaoka obtained jointly with Segawa and Jin necessary and sufficient conditions for the spaces of bounded harmonic functions (resp. harmonic functions with finite Dirichlet integrals) on Rand W being same, and in case R is the unit disc we obtained more results than that in the general case.
(2)In case p = 2,3, for -sheeted unlimited covering surfaces Rand R of C\{0} which are quasiconformally equivalent to each other, Masaoka showed jointly with Segawa that the harmonic dimension ( the cardinal number of the minimal Martin boundary) of R is equal to that of R'.
(3)For Heins' covering surfaces R and R' of C\{0} which are quasiconformally equivalent toeach other, Masaoka showed that the harmonic dimension of R is equal to that of R'
2.For a Denjoy domain Gin C with ρ boundary components (ρ≧3) and a Denjoy subdomain G'of G with ρ boundary components, Ishida showed that, if G' is mapped conformally into G by a mapping f preserving each boundary component, f is the identity mapping.
3.Tsuji studied the Cauchy problem for nonlinear second order hyperbolic equations.
4.Segawa studied the type problem for a infinitely sheeted simply connected unlimited covering surface of C.
5.Nishio obtained some characterizations for Caloric morphism brtween manifolds.

Report

(3 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • Research Products

    (39 results)

All Other

All Publications (39 results)

  • [Publications] Naondo Jin, Hiroaki Masaoka: "Kuramochi boundary and harmonic functions with finite Dirichlet integrals on unlimited covering surfaces"Osaka J.Math.. 41. 1-17 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hiroaki Masaoka, Shigeo Segawa: "Harmonic functions on finitely sheeted unlimited covering"J.Math.Soc.Japan. 55. 323-334 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 瀬川 重男, 正岡 弘照: "擬等角写像とC^^^\{0}のp葉非有界被覆面のミニマルなマルチン境界"数理解析研究所講究緑. 1293. 144-149 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 正岡 弘照, 神直人: "有限葉非有界被覆面の倉持極小境界点"数理解析研究所講究緑. 1293. 78-83 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hisashi Ishida, Fumio Maitani: "Conformal imbeddings of Denjoy domains II"Acta Human.Sci.Univ.Sangio Kyotiensis. 31. 1-5 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Mikio Tsuji: "Some remarks on nonlinear hyperbolic equations and systems"Abstract and applied analysis (World Scientific, edited by L.Nirenberg, W.Tutschke and N.M.Choung). (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Mikio Tsuji: "Integration and singularities of solutions for nonlinear second order hyperbolic equations"Differential operators and mathematical physics (edited by V.Ancona and J.Vaillant, Marcel Dekker). 109-127 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Nguyen Duy Thai Son, Mikio Tsuji: "Geometric solutions of nonlinear second order hyperbolic equations"Acta Mathematica Vietnamica. 27. 97-117 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Mikio Tsuji: "Geometric approach to certain systems of conservation laws"数理解析研究所講究緑. 1260. 24-32 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 中井三留, 瀬川重男: "被覆面の型"数理解析研究所講究緑. 1277. 84-93 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Masaharu Nishio, Katsunori Shimomura: "A characterization of caloric morphisms between manifolds"Ann.Acad.Sci.Fenn.Math.. 28. 111-122 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Masaharu Nishio, Katsunori Shimomura: "Caloric morphisms on semi-euclidean space"Rev.Roumaine Math.Pures Appl.. 47. 727-736 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Teruo Ikegami, Masaharu Nishio: "Q-compactification of harmonic spaces and the Choquet simplex"Osaka J.Math.. 39. 931-944 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Naondo Jin, Hiroaki Masaoka: "Kuramochi boundary and harmonic functions with finite Dirichlet integrals on unlimited covering surfaces"Osaka J.Math.. vol.41. 1-17 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hiroaki Masaoka, Shigeo Segawa: "Harmonic functions on finitely sheeted unlimited covering surfaces"J.Math.Soc.Japan. vol.55. 323-34 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Shigeo Segawa, Hiroaki Masaoka: "quasiconformal mapping and the minimal Martin boundary of p-sheeted unlimited covering surfaces of C {0}"RIMS kokyuroku. vol.1293. 78-83 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hiroaki Masaoka, Naondo Jin: "minimal Kuramochi boundary of finitely sheeted unlimited covering surfaces"RIMS kokyuroku. Vol.1293. 78-83 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hisashi Ishida, Fumio Maitani: "Conformal imbeddings of Denjoy domains II"Acta Human.Sci.Univ.Sangio Kyotiensis. vol.31. 1-5 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Mikio Tsuji: "Some remarks on nonlinear hyperbolic equations and systems"Abstract and applied analysis (World Scientific) (edited by L.Nirenberg, W.Tutschke, N.H.Chuong). (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Mikio Tsuji: "Integration and singularities of solutions for nonlinear second order hyperbolic equations"Differential operators and mathematical physics (edited by V.Ancona and J.Vaiflant, Marcel Dekker). 109-127 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Nguyen Duy Thai Son, Mikio Tsuji: "Geometric solutions of nonlinear second order hyperbolic equations"Acta Mathematica Vietnamica. vol.27. 97-117 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Mikio Tsuji: "Geometric approach to certain systems of conservation laws"RIMS kokyuroku. vol.1260. 24-32 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Mitsuru Nakai, Shigeo Segawa: "Type of covering surfaces"RIMS kokyuroku. Vol.1277. 84-93 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Masaharu Nishio, Katsunori Shimomura: "A characterization of caloric morphisms between manifolds"Ann.Acad.Sci.Fenn.Math.. vol.28. 111-122 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Masaharu Nishio, Katsunori Shimomura: "Caloric morphisms on semi-euclidean space"Rev.Roumaine Math.Pures Appl.. vol.47. 727-736 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Teruo Ikegami, Masaharu Nishio: "Q-compactiflcation of harmonic spaces and the Choquet simplex"Osaka J.Math.. vol.39. 931-944 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] N.Jin, H.Masaoka: "Kuramochi boundary and harmonic functions with finite Dirichlet integrals on unlimited covering surfaces"Osaka J.Math.. 141. (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Masaoka, S.Shigeo: "Harmonic functions on finitely sheeted unlimited covering surfaces"J.Math.Soc.Japan. 55. 323-334 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Tsuji: "Some remarks on nonlinear hyperbolic equations and systems"Abstract and applied analysis (World Scientific). (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Tsuji: "Integration and singularities of solutions for nonlinear second order hyperbolic equations"Differential operators and mathematical physics (edited by V.Ancona and J.Vaillant, Marcel Dekker). 109-127 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Nishio, K.Shimomura: "A characterization of caloric morphisms between manifolds"Ann.Acad.Sci.Fenn.Math.. 28. 111-122 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Hiroaki Masaoka, Shigeo Segawa: "Harmonic functions on finitely sheeted unlimited covering surfaces"Journal of the Math.Soc.Japan. 55(to appear). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] 瀬川 重男, 正岡 弘照: "擬等角写像とC^^^\{0}のp葉非有界被覆面のミニマルなマルチン境界"数理解析研究所講究録. 1293. 144-149 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 正岡 弘照, 神 直人: "有限葉非有界被覆面の倉持極小境界点"数理解析研究所講究録. 1293. 78-83 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Hisashi Ishida, Fumio Maitani: "Conformal imbeddings of Denjoy domains II"Acta Human.Sci.Univ.Sangio Kyotiensis. 31. 1-5 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Mikio Tsuji: "Geometric solutions of nonlinear second order hyperbolic equations"Acta Mathematica Vietnamica. 27. 97-117 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Mikio Tsuji: "Geometric approach to certain systems of conservation laws"数理解析研究所講究録. 1260. 24-32 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 中井三留, 瀬川重男: "被覆面の型"数理解析研究所講究録. 1277. 84-93 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Masaharu Nishio, Katsunori Shimomura: "A characterization of caloric morphisms between manifolds"Annales Academiase Scientiarum Fennicae Mathematica. Vol.28. 111-122 (2003)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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