| ON THE WILLMORE’S THEOREM FOR CONVEX HYPERSURFACES |
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| 引用本文： | 周家足.ON THE WILLMORE’S THEOREM FOR CONVEX HYPERSURFACES[J].数学物理学报(B辑英文版),2011,31(2):361-366. |
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| 作者姓名： | 周家足 |
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| 作者单位： | School of Mathematics and Statistics;Southwest University;Southeast Guizhou Vocational College of Technology for Nationalities; |
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| 基金项目： | Supported in part by CNSF (10671197) |
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| 摘 要： | Let M be a compact convex hypersurface of class C2, which is assumed to bound a nonempty convex body K in the Euclidean space Rn and H be the mean curvature of M. We obtain a lower bound of the total square of mean curvature M H2dA. The bound is the Minkowski quermassintegral of the convex body K. The total square of mean curvature attains the lower bound when M is an (n-1)-sphere.
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| 关 键 词： | 凸超曲面 定理 莫尔 作者 平均曲率 面积约束 闵可夫斯基 欧氏空间 |
On the Willmore's Theorem for convex hypersurfaces |
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| Zhou Jiazu School of Mathematics , Statistics,Southwest University,Chongqing ,China Southeast Guizhou Vocational College of Technology for Nationalities,Kaili ,China.On the Willmore's Theorem for convex hypersurfaces[J].Acta Mathematica Scientia,2011,31(2):361-366. |
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| Authors: | Zhou Jiazu School of Mathematics Statistics Southwest University Chongqing China Southeast Guizhou Vocational College of Technology for Nationalities Kaili China |
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| Institution: | Zhou Jiazu School of Mathematics and Statistics,Southwest University,Chongqing 400715,China Southeast Guizhou Vocational College of Technology for Nationalities,Kaili 556000,China |
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| Abstract: | Let M be a compact convex hypersurface of class C2, which is assumed to bound a nonempty convex body K in the Euclidean space Rn and H be the mean curvature of M. We obtain a lower bound of the total square of mean curvature M H2dA. The bound is the Minkowski quermassintegral of the convex body K. The total square of mean curvature attains the lower bound when M is an (n-1)-sphere. |
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| Keywords: | Mean curvature the Willmore deficit Minkowski quermassintegrale |
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