Researches on holomorphic mapings of Riemann surfaces---existence of mappings and conformal invariants
| Project/Area Number |
26400140
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Yamaguchi University |
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Principal Investigator |
MASUMOTO Makoto 山口大学, 大学院創成科学研究科, 教授 (50173761)
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| Co-Investigator(Kenkyū-buntansha) |
柴 雅和 広島大学, 工学研究科, 名誉教授 (70025469)
山田 陽 東京学芸大学, 教育学部, 名誉教授 (60126331)
柳原 宏 山口大学, 大学院創成科学研究科, 教授 (30200538)
中村 豪 愛知工業大学, 工学部, 教授 (50319208)
郷間 知巳 山口大学, 大学院創成科学研究科, 助手 (70253135)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | リーマン面 / 正則写像 / 等角写像 / 極値的長さ / 双曲的長さ / 穴あきトーラス |
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| Outline of Final Research Achievements |
A once-holed torus is, by definition, a Riemann surface homeomorphic to a once-punctured torus. The space T of once-holed tori with marked handle is identified with a smooth closed domain in the 3-dimensional euclidean space. Now, fix a Riemann surface Y with marked handle. We investigate the set A of elements X in T which allow holomorphic mappings into Y, and prove that it is a closed domain with Lipschitz boundary and is homeomorphic to T. Moreover, the boundary of A is not smooth in some cases. We also consider the set B of of elements X in T that are
conformally embedded into Y, and obtain similar results for B.
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Report
(5 results)
Research Products
(67 results)
