| 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)
徳永 宏 京都工芸繊維大学, 工芸学部, 教授 (10027906)
長町 重昭 徳島大学, 工学部, 教授 (00030784)
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| Project Period (FY) |
1999 – 2002
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| Project Status |
Completed (Fiscal Year 2002)
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| Budget Amount *help |
¥12,300,000 (Direct Cost: ¥12,300,000)
Fiscal Year 2002: ¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 2001: ¥3,900,000 (Direct Cost: ¥3,900,000)
Fiscal Year 2000: ¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 1999: ¥3,000,000 (Direct Cost: ¥3,000,000)
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| Keywords | Rigmann surfaces / Conformal embedding / Univalent functions / Analytic continuation / Fluid dynamics / Quadratic differentials / Fundamental domains / Hyperbolically maximal domains / 正則な単射 / 自己等角写像群 / 双曲的計量 / 双曲的極大領域 / ワイアシュトラスのゼータ関数 / トーラスのモジュラス / 流れのエネルギー / 理想境界の大きさ / 理想境界を越える解析接続 / 正則写像 / モジュラス / 理想境界 / 双曲的距離 / 不連続群の基本領域 |
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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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