ON THE WILLMORE'S THEOREM FOR CONVEX HYPERSURFACES

被引：0

作者：

Zhou Jiazu ^{[1
,2
]}

机构：

[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

[2] SE Guizhou Vocat Coll Technol Nationalities, Kaili 556000, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2011年 / 31卷 / 02期

关键词：

Mean curvature; the Willmore deficit; Minkowski quermassintegrale;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let M be a compact convex hypersurface of class C-2, which is assumed to bound a nonempty convex body K in the Euclidean space R-n and H be the mean curvature of M. We obtain a lower bound of the total square of mean curvature integral(M) H(2)dA. 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.

引用

页码：361 / 366

页数：6

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