ON THE WILLMORE'S THEOREM FOR CONVEX HYPERSURFACES

doi:10.1016/S0252-9602(11)60237-3

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (2): 361-366.doi: 10.1016/S0252-9602(11)60237-3

ON THE WILLMORE'S THEOREM FOR CONVEX HYPERSURFACES

周家足

School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
Southeast Guizhou Vocational College of Technology for Nationalities, Kaili |556000, China

收稿日期:2007-07-05 出版日期:2011-03-20 发布日期:2011-03-20
基金资助:
Supported in part by CNSF (10671197)

ON THE WILLMORE'S THEOREM FOR CONVEX HYPERSURFACES

ZHOU Jia-Zu

School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
Southeast Guizhou Vocational College of Technology for Nationalities, Kaili |556000, China

Received:2007-07-05 Online:2011-03-20 Published:2011-03-20
Supported by:
Supported in part by CNSF (10671197)

摘要/Abstract

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.

关键词: Mean curvature, the Willmore deficit, Minkowski quermassintegrale

Abstract:

Key words: Mean curvature, the Willmore deficit, Minkowski quermassintegrale

中图分类号:

52A20|

周家足. ON THE WILLMORE'S THEOREM FOR CONVEX HYPERSURFACES[J]. 数学物理学报(英文版), 2011, 31(2): 361-366.

ZHOU Jia-Zu. ON THE WILLMORE'S THEOREM FOR CONVEX HYPERSURFACES[J]. Acta mathematica scientia,Series B, 2011, 31(2): 361-366.

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ON THE WILLMORE'S THEOREM FOR CONVEX HYPERSURFACES

ON THE WILLMORE'S THEOREM FOR CONVEX HYPERSURFACES

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