2012 Fiscal Year Final Research Report
Stability and bifurcation for periodic minimal surfaces and surfaces with constant mean curvature, and applications to other fields
| Project/Area Number |
22654009
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Kyushu University |
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Principal Investigator |
KOISO Miyuki 九州大学, マス・フォア・インダストリ研究所, 教授 (10178189)
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| Co-Investigator(Renkei-kenkyūsha) |
YAMADA Kotaro 東京工業大学, 大学院・理工学研究科, 教授 (10221657)
SHODA Toshihiro 佐賀大学, 文化教育学部, 准教授 (10432957)
FUJIMORI Shoichi 岡山大学, 大学院・自然科学研究科, 准教授 (00452706)
KAWAKUBO Satoshi 福岡大学, 理学部, 助教 (80360303)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 極小曲面 / 平均曲率一定曲面 / 分岐理論 / 安定性 / 非等方的平均曲率一定曲面 / Wulff 図形 / ローレンツ・ミンコフスキー空間 / 非等方的極小曲面 |
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| Research Abstract |
We studied surfaces with constant mean curvature and surfaces with constant anisotropic mean curvature with free or fixed boundary. We obtained results about existence, uniqueness, geometric properties of solutions or stable solutions. Also, we obtained sufficient conditions for the existence of bifurcationand criterion of the stability for each surface in the bifurcation branch. Moreover,by removing the convexity assumption for the anisotropic surface energy, we studied uniformly a large class of surfaces including constant mean curvature surfaces in the Lorentz-Minkowski space and obtained a new uniqueness theorem and examples.
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