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Research on Martin and Kuramochi boundaries of covering surfaces

Research Project

Project/Area Number 12640193
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

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

Co-Investigator(Kenkyū-buntansha) SAGAWA Shigeo  Daido Institute of Technology, Faculty of Engineering, Professor, 工学部, 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)
NISHIO Masaharu  Osaka City University, Faculty of Science, Associate professor, 大学院・理学研究科, 助教授 (90228156)
Project Period (FY) 2000 – 2001
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 2001: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2000: ¥1,300,000 (Direct Cost: ¥1,300,000)
Keywordscovering surface / bounded harmonic function / Martin boundary / Dirichlet integral / Kuramochi boundary / Denjoy domain / nonlinear hyperbolic equation / Loeb's compactification / Dirichlet積分有限な調和関数 / 開リーマン面 / 極小マルチン境界 / 有限葉非有界被覆面 / 極小細位相 / 極小倉持境界点 / リーマン球面から原点をとり除いた面 / 擬等角写像 / Heins型被覆面
Research Abstract

1. (1) For a Riemann surface R and a finitely sheeted unlimited covering surface W of R, by Martin boundaries of R and W, Masaoka obtained jointly with Segawa a necessary and sufficient condition for the spaces of bounded harmonic functions on R and W being same.
(2) For a Riemann surface R, a finitely sheeted unlimited covering surface W of R and a minimal Kuramochi boundary point p of R, by minimal fine topology, Masaoka obtained jointly with Segawa a charcterization of the number of minimal Kuramochi boundary points of W over p.
(3) For a Riemann surface R, a finitely sheeted unlimited covering surface W of R and a minimal Martin boundary point p of R, by minimal fine topology, Masaoka obtained jointly with Segawa a characterization of the number of minimal Martin boundary points of W over p.
(4) For a Riemann surface R and a finitely sheeted unlimited covering surface W of R, by Kuramochi boundaries of R and W, Masaoka obtained a necessary and sufficient condition for the spaces of harmonic functions with finite Dirichlet integrals on R and W being same.
2. Ishida showed that, for a Denjoy domain G in C with n boundary components (n 【greater than or equal】 3) and a Denjoy subdomain G' of G with n boundary components such that G' is mapped conformally into G by a map f, G / f(G') has no interior points.
3. Tsuji studied the Cauchy problem for nonlinear hyperbolic equations.
4. Segawa studied the type problem for a infinitely sheeted simply connected unlimited covering surface of the Riemann sphere.
5. (1) Nishio gave a mean value property for solutions of parabolic equation of order α.
(2) Nishio showed that, under an appropriate condition, for the Martin's and Loeb's compactifications of a harmonic space in the sense of Brelot, their harmonic boundaries coincide.

Report

(3 results)
  • 2001 Annual Research Report   Final Research Report Summary
  • 2000 Annual Research Report
  • Research Products

    (33 results)

All Other

All Publications (33 results)

  • [Publications] 瀬川重男, 正岡弘照: "Bounded harmonic functions on unlimited covering surfaces"数理解析研究所講究録. 1137. 86-98 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Naondo Jin, Hiroaki Masaoka, Shigeo Segawa: "Kuramochi boundary of unlimited covering surfaces"Analysis. 20. 163-190 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Hiroaki Masaoka, Shigeo Segawa: "Martin boundary of unlimited covering surfaces"Journal D'analyse Math.. 82. 55-72 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Hisashi Ishida, Fumio Maitani: "Conformal imbeddings of Denjoy domains"Acta Human.Sci.Univ.Sangio Kyotiensis. 30. 1-7 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Hisashi Ishida, Fumio Maitani: "Conformal imbeddings of Denjoy domains II"Acta Human.Sci.Univ.Sangio Kyotiensis. 31(to appear). (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Mikio Tsuji: "Singularities of solutions for nonlinear hyperbolic equations of second order"Direct and inverse problems of mathmatical physics (edited by R.Gilbert et al., published by Kluwer Academic Publishers). 393-413 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Mikio Tsuji: "Hyperbolic equations, waves and the singularity theory"Functional-Analytic and complex methods, their interactions, and Applications to Partial Differential Equations (edited by H.Florian et al., published by World Scientific). 3-22 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 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, Kluwer Academic Publishers). (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 瀬川重男, 中井三留: "被覆面の型"数理解析研究所講究録. (掲載予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Masaharu Nishio, Noriaki Suzuki: "A characterization of strip domains by a mean value property for the parabolic operator of order α"New Jealand J.Math.. 29. 47-54 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Teruo Ikegami, Masaharu Nishio: "Q-compactification of harmonic spaces and the Choquet simplex"Osaka J.Math.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Hiroaki Masaoka and Shigeo Segawa: "Bounded harmonic functions on unlimited covering surfaces"RIMS kokyuroku. Vol. 1137. 86-98 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Naondo Jin, Hiroaki Masaoka and Shigeo Segawa: "Kuramochi boundary of unlimited covering surfaces"Analysis. Vol. 20. 163-190 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Hiroaki Masaoka and Shigeo Segawa: "Martin boundary of unlimited covering furfaces"Journal D'analyse Math.. Vol. 82. 55-72 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Hisashi Ishida and Fumio Maitani: "Conformal imbeddings of Denjoy domains"Acta Human Sci. Univ. Sangio Kyotiensis. Vol. 30. 1-7 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Hisashi Ishida and Fumio Maitani: "Conformal imbeddings of Denjoy domains II"Acta Human Sci. Univ. Sangio Kyotiensis. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Mikio Tsuji: "Singularities of solutions for nonlinear hyperbolic equations of second order"Direct and inverse problems of mathmatical phjysics (edited by R. Gilbert et al, published by Kluwer Academic Publishers). 393-413 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Mikio Tsuji: "Hyperbolic equations, waves and the singularity theory"Functional-Analytic and complex methods, their interactions, and Applications to Partial Differential Equations (edited by H. Florian et al, published by World Scientific). 3-22 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Mikio Tsuji: "Integration and singularities of solutions for nonlinear second order hyperbolic equations"Differential operators and mathematical physids (edited by V. Ancona and J. Vaillant, Kluwer Academic Publishers). (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Shigeo Segawa and Mitsuru Nakai: "Type of covering sufaces"RIMS kokyurokru. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Masaharu Nishio and Noriaki Suzuki: "A characterization of strip domains by a mean value property for the parabolic operator of order α"New Jealand J. Math.. Vol. 29. 47-54 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Teruo Ikegami and Masaharu Nishio: "Q-compactification of harmonic spaces and the Choquet simplex"Osaka J. Math.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Hisashi Ishida, Fumio Maitani: "Conformal imbeddings of Denjoy domains"Acta Human. Sci. Univ. Sangio Kyotiensis. 30. 1-7 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Hisashi Ishida, Fumio Maitani: "Conformal imbeddings of Denjoy domains II"Acta Human. Sci. Univ. Sangio Kyotiensis. 31(to appear). (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] Mikio Tsuji: "Hyperbolic equations, waves and the singularity theory""Functional-Analytic and complex methods, their interactions, and Applications to Partial Differential Equations", edited by H. Florian etc. 3-22 (2001)

    • Related Report
      2001 Annual Research Report
  • [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 (Kluwer Academic Publishers). (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] 瀬川重男, 中井三留: "被覆面の型"数理解析研究所講究録. (掲載予定).

    • Related Report
      2001 Annual Research Report
  • [Publications] Teruo Ikegami, Masaharu Nishio: "Q-compactification of harmonic spaces and the Choquet simplex"Osaka J. Math.. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] H.Masaoka and S.Shigeo: "Martin boundary of unlimited covering surfaces"Journal D'analyse Math.. 82. 55-72 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] N.Jin,H.Masaoka and S.Shigeo: "Kuramochi boundary of unlimited covering surfaces"Analysis. 20. 163-190 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Ishida and H.Maitani: "Conformal imbeddings of Denjoy domains"Acta Human.Sci.Univ.Sangio Kyotiensis. (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] M.Tsuji: "Singularities of solutions for nonlinear hyperbolic equations of second order""Direct and inverse problems of mathmatical physics" (edited by R.Gilbert et al, published by Kluwer Acad. Publisher). 393-413 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] M.Nishio and N.Suzuki: "A characterization of strip domains by a mean value property for the parabolic operator of order α"New Nealand J.Math.. 29. 47-54 (2000)

    • Related Report
      2000 Annual Research Report

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Published: 2000-04-01   Modified: 2016-04-21  

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