• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Variational Formula for Quasiconformal Mappings

Research Project

Project/Area Number 10640173
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

YANAGIHARA Hiroshi  Yamaguchi University, Faculty of Engineering, Associate Professor, 工学部, 教授 (30200538)

Co-Investigator(Kenkyū-buntansha) MASUMOTO Makoto  Yamaguchi University, Faculty of Science, Associate Professor, 理学部, 助教授 (50173761)
KATO Takao  Yamaguchi University, Faculty of Science, Professor, 理学部, 教授 (10016157)
KURIYAMA Ken  Yamaguchi University, Faculty of Engineering, Professor, 工学部, 教授 (10116717)
GOUMA Tomomi  Yamaguchi University, Faculty of Science, Research Associate, 理学部, 助手 (70253135)
KIUCHI Isao  Yamaguchi University, Faculty of Science, Associate Professor, 理学部, 助教授 (30271076)
松野 好雅  山口大学, 工学部, 教授 (30190490)
柳 研二郎  山口大学, 工学部, 教授 (90108267)
Project Period (FY) 1998 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥3,800,000 (Direct Cost: ¥3,800,000)
Fiscal Year 1999: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1998: ¥2,200,000 (Direct Cost: ¥2,200,000)
Keywordssingular integral / quasiconformal mapping / variational formula / Beltrami differential / Bloch functions / distortion estimate / growth estimate / global solutions
Research Abstract

Let SィイD1pィエD1(C) = LィイD1pィエD1(C, (π(1 + |z|ィイD12ィエD1)ィイD12ィエD1)ィイD1-1ィエD1dxdy) be the space of p-th integrable functions with respect to the spherical metric on the Riemann sphere C. Let T be an variant of the Ahlfors-Beurling operator defined by
<<numerical formula>>.
Theorem 1 Let p 【not a member of】(2, ∞). Then for u 【not a member of】 SィイD1pィエD1(C), Tu(z) exists almost everywhere. Furthermore There exists CィイD2pィエD2 > 0 such that
<<numerical formula>>.
Theorem 2 Let p 【not a member of】 (2, ∞) Then for all μ 【not a member of】 LィイD1∞ィエD1(C) with ||μ||ィイD2∞ィエD2 < min{1/C(p), 1/3} μ-quasiconformal automorphism f of C can be expanded as follows,
<<numerical formula>>,
where the series converges absolutely in SィイD1pィエD1(C).

Report

(3 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] H.Yanagihara: "On the growth of Bloch functions"Complex Variables. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 劉 承論,栗山 憲,水田 義明: "3次元非定常熱伝導解析の為の境界要素法を用いた直接法解析コードの開発"資源と素材. 114-4. 225-228 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] T.Kato and C.Keem: "G.Martense' dimension thoerem for curves of odd gonality"Geom.Dedicata. 78. 301-313 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M.Masumoto: "Extremal lengths of homology classes on Riemann surface"J.Reine Angew.Math.. 508. 17-45 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] I.Kiuchi and Y.Taniigawa: "The mean value theorem of the divisor probrem for short intervals"Archiv der Math.. 71. 445-453 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] T.Gouma: "Ahlfors functions on non-planar Riemann surfaces whose double are hyperellipt ic"J.Math.Soc.Japan. 50. 685-695 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Hiroshi Yanagihara: "On the growth of Bloch functions"Complex Voariables. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] L. Zhang, H. Miike and K. Kuriyama: "The spatio-temporal optimization to determine optical flow with combination of local and global approach"Forma. 13. 229-320 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] T. Kato and C. Keem: "G. Martense' dimension thoerem for curves of odd gonality"Geom. Dedicata. 78. 301-313 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M. Masumoto: "Extremal lengths of homology classes on Riemann surface"J. fur Reine Angew. Math.. 508. 17-45 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] I. Kiuchi and Y. Tanigawa: "The mean value theorem of the divisor probrem for short intervals"Archiv der Math.. 71. 445-453 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] T. Gouma: "Ahlfors functions on non-planar Riemam surfaces whose double are hyperelliptic"J. Math. Soc. Japan. 50. 685-695 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H.Yanagihara: "On the growth of Bloch functions"Complex Variables. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] 劉 承論,栗山 憲,水田 義明: "3次元非定常熱伝導解析の為の境界要素法を用いた直接法解析コードの開発"資源と素材. 114-4. 225-228 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] T.Kato and C.Keem: "G.Martense' dimension thoerem for curves of odd gonality"Geom.Dedicata. 78. 301-313 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] M.Masumoto: "Extremal lengths of homology classes on Riemann surface"J.Reine Angew.Math.. 508. 17-45 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] I.Kiuchi and Y.Tanigawa: "The mean value theorem of the divisor probrem for short intervals"Archiv der Math.. 71. 445-453 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] T.Gouma: "Ahlfors functions on non-planar Riemann surfaces whose double are hyperelliptic"J.Math.Soc.Japan. 50. 685-695 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] K.Yanagi: "An upper bound to the capacity of discrete time Gaussian channel with feedback,III" Bull.Kyushu Inst.Tech.45. 1-8 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.W.Chen and K.Yanagi: "Refinement of factor-of-two bound for capacity in Gaussian channel with feedback and related inequality" Proceedings on 1998 International Symposium on Information The-ory. 128- (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Y.Matsuno: "The small dispersion limit of the Benjamin-Ono equation and the evolution of the step initial condition" Journal of the Physical Society of Japan. 67. 1814-1817 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Hayashi and K.Kato: "Point separation of a two-sheeted disc by boounded abalytic functions" Hokkaido Math.J.Proc.27. 553-565 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Kato,C.Keem and A.Ohbuchi: "Variety of special linear systems on k-sheeted coverings" Geom.Dedicata. 69. 53-65 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Gouma: "Ahlfors functions on non-planar Riemann surfaces whose double are hyperelliptic" J.Math.Soc.Japan. 50. 685-695 (1998)

    • Related Report
      1998 Annual Research Report

URL: 

Published: 1998-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi