Researches of principal distributions and over-determined systems on surfaces
| Project/Area Number |
21740054
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Kumamoto University |
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Principal Investigator |
ANDO Naoya 熊本大学, 大学院・自然科学研究科, 准教授 (50359965)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 曲面 / 主分布 / 優決定系(過剰決定系) / 準曲面 / 多項式型 / 整合条件 / 主方向 / Hessian / 指数予想 / Loewnerの予想 / 平坦な計量 / 第一基本形式 / Hopf微分 / 双曲型偏微分方程式 / 非等方的平均曲率一定曲面 / Hartman-Wintnerの定理 / 優決定系 / 極小曲面 |
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| Research Abstract |
I characterized minimal surfaces in E^3 in terms of over-determined systems on surfaces. I devised two generalizations of an over-determined system on a surface and obtained several results which are considered as generalizations of results I already had with respect to over-determined systems on surfaces. I presented another proof of a result by Koiso-Palmer with respect to surfaces with constant anisotropic mean curvature. I locally represented principal distributions on a surface as fields obtained from eigendirections of the Hessian of some function with respect to the first fundamental form of the surface.
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Report
(4 results)
Research Products
(22 results)
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[Presentation] 曲面上の主分布の振る舞い2010
Author(s)
安藤直也
Organizer
日本数学会2010年度年会幾何学分科会特別講演
Place of Presentation
慶應義塾大学(神奈川,矢上キャンパス)
Year and Date
2010-03-24
Related Report
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