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2004 Fiscal Year Final Research Report Summary

A study on the holomorphic mappings on the unit ball

Research Project

Project/Area Number 14540195
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionKyushu Sangyo University (2003-2004)
Kyushu Kyoritsu University (2002)

Principal Investigator

HAMADA Hidetaka  Kyushu Sangyo University, Faculty of Engineering, Professor, 工学部, 教授 (30198808)

Project Period (FY) 2002 – 2004
Keywordsholomorphic mapping / biholomorphic mapping / quasiconformal / quasiconformal extension / proper holomorphic mapping / rational mapping
Research Abstract

1.We give a sufficient condition that the first element of a Loewner chain on the Euclidean unit ball can be extended to a quasiconformal homeomorphism of C^n onto itself.
2.We give sufficient conditions for locally biholomorphic mappings on the unit ball in a complex Banach space to be starlike of certain order or strongly starllke.
3.We obtain sufficient conditions for biholomorphic mappings on the unit ball of a complex Banach space to have parametric representation.
4.We consider the generalization of the Loewner differential equation to reflexive complex Banach spaces. We obtain some Lipechitz continuity results related to Loewner chains and their transition mappings.
5.We give a sharp lower bound for the distortion of the image of the Roper-Suffridge extension operator : This result gives a positive answer to an open problem posed by Liczberski-Starkov.
6.We give a complete classification of rational proper holomorphic maps from B^n into B^<2n> when n>3.
7.Pescar investigated the univalence of certain integral operators. We show that the results are obtained by the Schwarz lemma. We also give some generalizations.
8.Let f(z,t) be a subordination chain on[0,α] on the Euclidean unit ball B in C^n. We give a sufficient condition that f can be extended to a quasiconformal homeomorphism of R^<2n> onto itself.
9.We give coefficient conditions for some rational mappings to be starlike or convex on the Euclidean unit ball B in C^n.

  • Research Products

    (14 results)

All 2005 2004 2003 Other

All Journal Article (14 results)

  • [Journal Article] Rational proper holomorphic maps from B^n into B^<2n>2005

    • Author(s)
      H.Hamada
    • Journal Title

      Mathematische Annalen 331

      Pages: 693-711

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Loewner chains and parametric representation of biholomorphic mappings in complex Banach spaces2004

    • Author(s)
      H.Hamada, G.Kohr
    • Journal Title

      Glasnik Matematicki 39(59)

      Pages: 55-72

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Loewner chains and the Loewner differential equation in reflexive complex Banach spaces2004

    • Author(s)
      H.Hamada, G.Kohr
    • Journal Title

      Rev.Roumaine Math.Pures Appl. 49

      Pages: 247-264

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Roper-Suffridge extension operator and the lower bound for the distortion2004

    • Author(s)
      H.Hamada, G.Kohr
    • Journal Title

      Journal of Mathematical Analysis and Applications 300

      Pages: 454-463

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Loewner chains and quasiconformal extension of holomorphic mappings2003

    • Author(s)
      H.Hamada, G.Kohr
    • Journal Title

      Ann.Polon.Math. 81

      Pages: 85-100

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Simple criterions for strongly starlikeness and starlikeness of certain order2003

    • Author(s)
      H.Hamada, G.Kohr
    • Journal Title

      Math.Nachr. 254-255

      Pages: 165-171

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Loewner chains and quasiconformal is extension of holomorphic mappings2003

    • Author(s)
      H.Hamada, G.Kohr
    • Journal Title

      Ann.Polon.Math. 81

      Pages: 85-100

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Simple criterions for strongly starlikeness and starlikeness of certain order2003

    • Author(s)
      H.Hamada, G.Kohr
    • Journal Title

      Math.Nachr. 254 255

      Pages: 165-171

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Univalence criterion for certain integral operators

    • Author(s)
      H.Hamada
    • Journal Title

      Demonstratio Mathematica To Appear

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A class of rational functions in several complex variables

    • Author(s)
      H.Hamada, G.Kohr
    • Journal Title

      Demonstratio Mathematica To Appear

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Quasiconformal extension of biholomorphic mappings in several complex variables

    • Author(s)
      H.Hamada, G.Kohr
    • Journal Title

      Journal d'Analyse Mathematique To Appear

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Univalence criterion for certain integral operators

    • Author(s)
      H.Hamada
    • Journal Title

      Demonstratio Mathematica (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] A class of rational functions in several complex variables

    • Author(s)
      H.Hamada, G.Kohr
    • Journal Title

      Demonstratio Mathematica (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Quasiconformal extension of biholomorphic mappings in several complex variables

    • Author(s)
      H.Hamada, G.Kohr
    • Journal Title

      Journal d'Analyse Mathematique (to appear)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2006-07-11  

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