| Project/Area Number |
09640106
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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 |
Geometry
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| Research Institution | HIROSHIMA UNIVERSITY (1998)
Osaka University (1997) |
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Principal Investigator |
UMEHARA Masaaki Fac.Sci., HIROSHIMA UNIVERSITY Prof., 理学部, 教授 (90193945)
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| Co-Investigator(Kenkyū-buntansha) |
KOWATA Asutaka Fac.Sci., HIROSHIMA UNIVERSITY Research Associate, 理学部, 助手 (50033931)
DOI Hideo Fac.Sci., HIROSHIMA UNIVERSITY Lecturer, 理学部, 講師 (50197993)
KOISO Norihito Osaka U., Grad.School Sci., Prof., 大学院・理学研究科, 教授 (70116028)
藤原 彰夫 大阪大学, 大学院・理学研究科, 講師 (30251359)
難波 誠 大阪大学, 大学院・理学研究科, 教授 (60004462)
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| Project Period (FY) |
1997 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 1998: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1997: ¥2,300,000 (Direct Cost: ¥2,300,000)
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| Keywords | Cuvue / Suvface / Vertex / Constant mean cuvuature / Conlcal Singularity / 双曲型空間 / 錐的特異点 |
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| Research Abstract |
We get the following results :
1. The head investigator Masaaki Umehara gave a flux formula for surfaces of constant mean curvature 1 (i.e. CMC-1 surfaces) in the hyperbolic 3-space as an analogy for that of minimal surfaces in the Euclidean space, which is a joint work with Wayne Rossman (Kobe Univ.) and Kotaro Yamada (Kumamoto Univ.). As an application, he and K.Yamada classified all conformal metrics of constant curvature 1 with three conical singularities on 2-sphere.
2. The head investigator Masaaki Umehara and Gudlaugur Thorbergs-son (Koln Univ.) gave a refinement of the classical four vertex theorem on simple closed curves, where they gave an abstract intrinsic approach regarding the theorem as a kind of homology theory on S^1 whose first Betti number is the number of vertices. As an application, they prove a four vertex theorem on some kind of space curves and also gave a new proof of the four vertex theorem for diffeo-morphisms on S^1. Moreover, they generalized the theory for much higher order geometry and gave sharp estimates for affine vertices on simple closed curves.
3. The investigator Koiso investigated the elasticas in a Riemannian manifolds by analytic approach.
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