| Project/Area Number |
11440048
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | HIROSHIMA UNIVERSITY |
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Principal Investigator |
SHIBA Masakazu Hiroshima University, Graduate School of Engineering, Professor, 大学院・工学研究科, 助教授 (70025469)
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| Co-Investigator(Kenkyū-buntansha) |
MIZUTA Yoshihiro Hiroshima University, Faculty of Integrated Arts and Sciences, Professor, 総合科学部, 教授 (00093815)
KANEKO Arata Hiroshima University, Graduate School of Engineering, Professor, 大学院・工学研究科, 教授 (10038101)
ITO Masaaki Hiroshima University, Graduate School of Engineering, Associate Professor, 大学院・工学研究科, 助教授 (10116535)
MAITANI Fumio Kyoto Institute of Technology, Faculty of Engineering, Professor, 工芸学部, 教授 (10029340)
MASUMOTO Makoto Yamaguchi University, Faculty of Science, Associate Professor, 理学部, 助教授 (50173761)
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| Project Period (FY) |
1999 – 2002
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| Keywords | Rigmann surfaces / Conformal embedding / Univalent functions / Analytic continuation / Fluid dynamics / Quadratic differentials / Fundamental domains / Hyperbolically maximal domains |
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| Research Abstract |
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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