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Analysis of quasisymmetric functions and Teichmuller space

Research Project

Project/Area Number 13640185
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionOsaka City University

Principal Investigator

SAKAN Ken-ichi  Osaka City University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (70110856)

Co-Investigator(Kenkyū-buntansha) 小森 洋平  大阪市立大学, 大学院・理学研究科, 講師 (70264794)
NISHIO Masaharu  Osaka City University, Graduate School of Science, Lecturer, 大学院・理学研究科, 助教授 (90228156)
IMAYOSHI Yoichi  Osaka City University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (30091656)
NAKANISHI Toshihiro  Nagoya University, Graduate School of Polymathematics, Associate Professor, 大学院・多元数理科学研究科, 助教授 (50701546)
TUGAWA Toshiyuki  Hiroshima University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (30235858)
吉田 雅通  大阪市立大学, 大学院・理学研究科, 助手 (60264793)
Project Period (FY) 2001 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 2003: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2002: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2001: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywordsquasisymmetric function / quasiconformal mapping / quasiconformal extension / extremal extension / crossratio / conjugte function / conjugate function / harmonic extension / Teichmuller space / 調和格調 / 擬対称自己同型
Research Abstract

The head investigator Sakan published jointly with the foreign joint worker D.Partyka "On pseudo-metrics on the space of generalized quasisymmetric automorphisms of a Jordan curve" and "On Heinz's inequality ". In the former paper they introduced, with no use of quasiconformal mappings, some pseudo-metrics into the space of generalized quasisymmetric automorphisms of a Jordan curve, and discussed some applications to topological properties of the Teichmiuller pseudo-metric. In the latter paper they generalized the Heinz's result on one-to-one harmonic mappings F of the unit disc onto itself in the case where F is the Poisson integral of a sense-preserving homeomorphic self-mapping of the unit circle. As an application they inferred a version of Heinz's inequality for harmonic and quasiconformal self-mappings of the unit disc. In a paper to be. submitted, they show an asymptotically sharp variant of Heinz's inequality for harmonic and quasiconformal self-mappings of the unit disc.
For the analysis of quasisymmetry, it is important to analyze the representations of maximal dilatations and so on in terms of harmonic measure and crossratio. Furthermore, it turned out that boundary dilatations, conjugate functions and Cauchy singular integrals are deeply related to the quasiconformality of harmonic extensions. Sakan has discussed about these analyses, with investigators Nishio and Yoshida from the viewpoint of potential and probability theory. Further, on extremal extensions which are quite related to boundary dilatations Sakan has contacted foreign joint workers Y.Shen, S.Wu and investigators Ohtake and Sugawa. Moreover, Sakan has discussed with investigators Imayoshi, Komori and Nakanishi about the relation of their researches on Teichmuller space and our research project.

Report

(4 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • Research Products

    (31 results)

All Other

All Publications (31 results)

  • [Publications] D.Partyka, K.Sakan: "On pseudo-metrics on the space of generalized quasisymmetric automorphisms of a Jordan curve"Ann.Univ.Mariae Curie-Sklodowska Sect, A. 55. 115-138 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] D.Partyka, K.Sakan: "On Heinz's inequality"Bull.Soc.Sci, Letters Lodz Ser.Rech.Deform.36. 52. 27-34 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Imayoshi, H.Ito, H.Yamamoto: "On the Nielsen-Thurston-Bers type of some self-maps of Riemann surfaces with two specific points"Osaka J.Math.. 40. 659-685 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Ikegami, M.Nishio: "Q-compectification 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] V.Gutlyanskii, T.Sugawa: "On Lipschitz continuity of quasiconformal mappings"Report.Univ.Jyvaskyla. 83. 91-108 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Sugawa: "A remark on the Ahlfors-Lehto univalence criterion"Ann.Acad.Sci.Fenn.Ser.A I Math.. 27. 151-161 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 今吉洋一, 佐官謙一, 西尾昌治, 小森洋平, 須川敏幸を含む10人の共訳: "ヴィジュアル複素解析.T.ニーダム著、共訳"培風館. 662 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Sakan, D.Partyka: "On pseudo-metrics on the space of generalized quasisymmetric automorphisms of a Jordan curve"Ann.Univ.Mariae Curie-Sklodowska Sect.A. 55. 115-138 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] K.Sakan, D.Partyka: "On Heinz's inequality"Bull.Soc.Sci.Letters Lodz Ser.Rech.Deform.. 36.52. 27-34 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Imayoshi, M.Ito, H.Yamamoto: "On the Nielsen-Thurston-Bers type of some self-maps of Riemann surfaces with two specified points"Osaka J.Math.. 40. 659-685 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Ikegami, M.Nishio: "Q-compactification of harmonic spaces and the Choquet simples"Osaka J.Math.. 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] V.Gutlyanskii, T.Sugawa: "On Lipschitz continuity of quasiconformal mappings"Report.Univ.Jyvaskyla. 83. 94-108 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Sugawa: "A remark on the Ahfors-Lehto univalence criterion"Ann Acad.Sci.Fenn.Ser.Al Math.. 27. 151-161 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] D.Portyka, K.Sakan: "On Heinz's Inequality"Bull.Soc.Sci.Lettres Lodz Ser.Rech.Deform.37. 52. 27-34 (2002)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Imayoshi, M.Ito, H.Yamamoto: "On the Nielsen-Thurston-Bers type of some self-maps of Riemann surfaces with two specified points"Osaka J.Math.. 40. 659-685 (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] Y.Komori: "On the boundary of the Earle slice for punctured torus groups, Kleinian groups and hyperbolic 3-manifolds"London Math.Soc.Lec.Notes. 299. 293-304 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Nakanishi, M.Naatanen: "穴あき曲面群のSL(2,C)表現とトレース恒等式,双曲空間に関連する研究とその展望"数理解析研究所講究録. 1329. 72-83 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] V.Gutlyanskii, O.Martio, T.Sugawa, M.Vuorinen: "On the existence and uniqueness theorems for the degenerate Beltrami equation"Dokl.Akad.Nauk. 393. 1-3 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] D.Parytka, K.Sakan: "On Heinz's inequality"Bull. Soc. Sci. Letters Lodz.. (発表予定).

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Ikegami, M.Nishio: "Q-compactification of harmonic spaces and the Choquet simplex"Oska J. Math.. 39. 931-944 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Komori: "On the boundary of the Earle slice for punctured torus groups"Proceedings of Minsky workshop (September-2001), LMS Lecture Notes, Kleinian groups and hyperbolic 3-manifolds. (発表予定).

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Naatanen, T.Nakanishi: "Areas of two-dimensional moduli spaces"Proc. Amer. Math. Soc.. 129. 3241-3252 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Sugawa: "Estimates of hyperbolic metric with applications to Teichmuller spaces"Kyungpook Math. J.. 42. 51-60 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Sugawa: "A remark on the Ahlfors-Lehto univalence criterion"Ann. Acad. Sci. Fenn. AI Math.. 27. 151-161 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] D.Partyka, K.Sakan: "On pseudo-metrics on the space of generalized quasisymmetric automorphisms of a Jordan curve"Ann.Univ.Mariae Curie-Sklodowska Sect.A. 55. 115-138 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] D.Partyka, K.Sakan: "On Heinz's inequality"Bull.Soc.Sci.Lettres Lodz.. (発表予定).

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.Imayoshi, M.Ito, H.Yamamoto: "A remark on the Bers type of some self-maps of Riemann surfaces with two specified points"International Society for Analysis, Applications and computation(Kluwer). 8. 871-875 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Ikegami, M.Nishio: "Q-compactification of harmonic spaces and the choquet simplex"Osaka J.Math.. (発表予定).

    • Related Report
      2001 Annual Research Report
  • [Publications] Y.komori, C.Series: "Pleating coordinates for the Earle embedding"Ann.Fac.Sci.Toulouse Math.. 10. 69-105 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] M.Naatanen, T.Nakanishi: "Areas of two-dimensional moduli spaces"Proc.Amer.Math.Soc.. 129. 3241-3252 (2001)

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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