The Willmore functional and the containment problem in R^4

作     者：Jia-zu ZHOU School of Mathematics and Statistics, Southwest University, Chongqing 400715, China Department of Mathematics, Polytechnic University, Brooklyn, NY 11201, USA 

作者机构：School of Mathematics and Statistics Southwest University Chongqing China Department of Mathematics Polytechnic University Brooklyn USA 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2007年第50卷第3期

页      面：325-333页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：This work was partially supported by the National Natural Science Foundation of China(Grant No.10671159) the Funds for Qualified Scientists and Technicians in Guizhou Province of China and Southwest University 

主　　题：mean curvature scalar curvature kinematic formula Minkowski quermassintegrals convex body convex hypersurface. 

摘      要：Let∑be a convex hypersurface in the Euclidean space R4 with mean curvature H. We obtain a geometric lower bound for the Willmore functional∫∑H2dσ. This bound is an invariant involving the area of∑, the volume and Minkowski quermassintegrals of the convex body that∑bounds. We also obtain a sufficient condition for a convex body to contain another in the Euclidean space R4.