2012 Fiscal Year Final Research Report
Analysis of gradient flow for the bending energy of plane curves under multiple constraints
| Project/Area Number |
22540219
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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 |
Global analysis
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| Research Institution | Saitama University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
KOIKE Shigeaki 埼玉大学・より東北大学, 大学院・理工学研究科, 教授 (90205295)
太田 雅人 埼玉大学・より東京理科大学, 大学院・理工学研究科・理学部, 准教授 (00291394)
阪本 邦夫 埼玉大学, 大学院・理工学研究科, 教授 (70089829)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 変分法 / 勾配流 / 制約条件 / Lagrangeの未定乗数 / 正則性 |
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| Research Abstract |
The Helfrich variational problem is one for the bending energy of closed plane curves under constrains of length and enclosed volume. The problem can be formulated not only for curves but also for surfaces and hypersurface, i.e., higher dimensional case. We study the behavior of the corresponding gradient flow, called the “Helfrich flow". Firstly, we construct the Helfrich flow of general dimension, and discuss the uniqueness. Furthermore we get a new fact on the global existence of generalized rotational hypersurface which is useful for the analysis of behavior for the Helfrich flow.
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