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

• 论文 • 上一篇    下一篇

ON THE WILLMORE'S THEOREM FOR CONVEX HYPERSURFACES

周家足   

  1. 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   

  1. 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:

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:

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.

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

中图分类号: 

  • 52A20|