2013 Fiscal Year Final Research Report
Research on holomorphic mappings of Riemann surfaces----roles of handles played in the existence problem of holomorphic mappings
| Project/Area Number |
22540196
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Yamaguchi University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
SHIBA Masakazu 広島大学, 工学研究科, 名誉教授 (70025469)
YAMADA Akira 東京学芸大学, 教育学部, 教授 (60126331)
YANAGIHARA Hiroshi 山口大学, 大学院理工学研究科, 准教授 (30200538)
HATAYA Yasushi 山口大学, 大学院理工学研究科, 准教授 (20294621)
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| Co-Investigator(Renkei-kenkyūsha) |
KIUCHI Isao 山口大学, 大学院理工学研究科, 教授 (30271076)
WATANABE Tadashi 山口大学, 教育学部, 教授 (10107724)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | リーマン面 / 正則写像 / 極値的長さ / 穴あきトーラス |
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| Research Abstract |
A Riemann surface is a connected complex manifold of dimension one, which is topologically an orientable surface and hence has several handles in general. A Riemann surface homeomorphic to the surface obtained from a torus by removing one point is called a once-holed torus. The once-holed tori make a space of real dimension three. In the present research we fix a Riemann surface Y with a marked handle. We investigate the set A of once-holed tori X for which there is a holomorphic mapping X into Y whose image corresponds to the marked handle, and compare A with the subset consisting of once-holed tori X which allow holomorphic mappings of finite degree into Y. It turns out that A is the closure of B and that B is a proper subset of A unless Y is a torus or a once-holed torus.
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Research Products
(51 results)
