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Theory of injective holomorphic mappings of a Riemann surface into another and its applications to hydrodynamics - a modern comprehension of the classical theory of univalent functions

Theory of injective holomorphic mappings of a Riemann surface into another and its applications to hydrodynamics - a modern comprehension of the classical theory of univalent functions
黎曼曲面到另一个曲面的单射全纯映射理论及其在流体动力学中的应用 - 对单价函数经典理论的现代理解
批准号:
11440048
负责人:
SHIBA Masakazu
金额:
$7.87万
依托单位:
依托单位国家:
日本
项目类别:
Grant-in-Aid for Scientific Research (B)
财政年份:
1999
资助国家:
日本
项目状态:
已结题
起止时间:
1999 至 2002

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中文摘要
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英文摘要
The principal aim of the project has been to generalize the classical theory of univalent functions to that of conformal embeddings of a Riemann surface into another, and to find a number of properties of such mappings which had never been observed in the classical case. We studied hydrodynamics on Riemann surfaces, particularly on a torus. We investigated a new type of extremal problem (with respect to the hyperbolic metric) to obtain the notion of "hyperbolically maximal domain". We proved that a hyperbolically maximal domain is a fundamental domain and its boundary consists of trajectory arcs of a meromorphic quadratic differential. We then gave a new construction of a fundamental domain for a Fuchsian group. We also studied the new concept of analytic continuation "beyond the ideal boundary".Part of the obtained results is reported in several international meetings: in Catania, Italy (2000), in Seoul, Korea (2001), Aveiro, Portugal (2001), and in Halle, Germany (2002).
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通讯作者:
S.Nagamachi: "Hyperfunction quantum field theory : Analytic structure, modular aspects, and local observable algebras"J. Math. Phys.. 42・1. 99-129 (2001)
S.Nagamachi:“超函数量子场论:解析结构、模方面和局部可观测代数”J. Math. 99-129。
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G.Schmieder: "On the Mobius distance"Annales UMCS, Sec.A. 54・11. 125-131 (2000)
G.Schmieder:“论莫比乌斯距离”Annales UMCS,Sec.A. 125-131 (2000)。
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T.Futamura: "A generalization of the Liouville theorem to polyharmonic functions"to appear in J.Math.Soc.Japan. 53. (2001)
T.Futamura:“刘维尔定理对多调和函数的推广”发表于 J.Math.Soc.Japan。
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212
    Study of the continuations and the spans of an open Riemann surface in view of the thory of functions of several complex variables
    • 批准号:
      15K04930
    • 项目类别:
      Grant-in-Aid for Scientific Research (C)
    • 资助金额:
      $2.91万
    • 财政年份:
      2015
    • 负责人:
      SHIBA Masakazu
    • 依托单位:
    Continuations of a Riemann surface and dynamics of viscos fluid --- study of conformal embeddings and associated Poiseuille flow
    • 批准号:
      20540174
    • 项目类别:
      Grant-in-Aid for Scientific Research (C)
    • 资助金额:
      $2.75万
    • 财政年份:
      2008
    • 负责人:
      SHIBA Masakazu
    • 依托单位:
    Study on the theory of conformal embeddings of a Riemann surface focused on the hyperrbolic metric and hydrodynamics of viscous fluids
    • 批准号:
      16540157
    • 项目类别:
      Grant-in-Aid for Scientific Research (C)
    • 资助金额:
      $2.37万
    • 财政年份:
      2004
    • 负责人:
      SHIBA Masakazu
    • 依托单位:
    Analysis on Riemann surfaces and manifolds to gether with contributions to physics and engineeing
    • 批准号:
      09640193
    • 项目类别:
      Grant-in-Aid for Scientific Research (C)
    • 资助金额:
      $1.98万
    • 财政年份:
      1997
    • 负责人:
      SHIBA Masakazu
    • 依托单位: