The Logarithmic Sobolev Inequality for a Submanifold in Manifolds with Nonnegative Sectional Curvature  

作　　者：Chengyang YI Yu ZHENG 

机构地区：[1]School of Mathematical Sciences,East China Normal University,Shanghai 200241,China

出　　处：《Chinese Annals of Mathematics,Series B》2024年第3期487-496,共10页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(No.12271163);the Science and Technology Commission of Shanghai Municipality(No.22DZ2229014);Shanghai Key Laboratory of PMMP.

摘　　要：The authors prove a sharp logarithmic Sobolev inequality which holds for compact submanifolds without boundary in Riemannian manifolds with nonnegative sectional curvature of arbitrary dimension and codimension.Like the Michael-Simon Sobolev inequality,this inequality includes a term involving the mean curvature.This extends a recent result of Brendle with Euclidean setting.

关 键 词：Logarithmic Sobolev inequality Nonnegative sectional curvature SUBMANIFOLD 

分 类 号：O186.1[理学—数学]