A note on the entropy of mean curvature flow  

作　　者：BAO Chao 

机构地区：[1]Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences,Peking University

出　　处：《Science China Mathematics》2015年第12期2611-2620,共10页中国科学：数学（英文版）

摘　　要：The entropy of a hypersurface is given by the supremum over all F-functionals with varying centers and scales, and is invariant under rigid motions and dilations. As a consequence of Huisken's monotonicity formula, entropy is non-increasing under mean curvature flow. We show here that a compact mean convex hypersurface with some low entropy is diffeomorphic to a round sphere. We also prove that a smooth selfshrinker with low entropy is a hyperplane.The entropy of a hypersurface is given by the supremum over all F-functionals with varying centers and scales, and is invariant under rigid motions and dilations. As a consequence of Huisken’s monotonicity formula, entropy is non-increasing under mean curvature flow. We show here that a compact mean convex hypersurface with some low entropy is diffeomorphic to a round sphere. We also prove that a smooth selfshrinker with low entropy is a hyperplane.

关 键 词：ENTROPY self-shrinker mean curvature flow SPHERE 

分 类 号：O186.1[理学—数学]