Intrinsic ultracontractivity on Riemannian manifolds with infinite volume measures  

作　　者：WANG FengYu 1,2 1 School of Mathematical Sciences,Beijing Normal University,Beijing 100875,China 2 Department of Mathematics,Swansea University,Singleton Park,Swansea SA2 8PP,UK 

出　　处：《Science China Mathematics》2010年第4期895-904,共10页中国科学：数学（英文版）

基　　金：supported by Science Fund for Creative Research Groups of National Natural Science Foundation of China (No.10121101);National Basic Research Program of China(Grant No.2006CB805901)

摘　　要：By establishing the intrinsic super-Poincar'e inequality,some explicit conditions are presented for diffusion semigroups on a non-compact complete Riemannian manifold to be intrinsically ultracontractive.These conditions,as well as the resulting uniform upper bounds on the intrinsic heat kernels,are sharp for some concrete examples.By establishing the intrinsic super-Poincar’e inequality,some explicit conditions are presented for diffusion semigroups on a non-compact complete Riemannian manifold to be intrinsically ultracontractive.These conditions,as well as the resulting uniform upper bounds on the intrinsic heat kernels,are sharp for some concrete examples.

关 键 词：INTRINSIC ultracontractivity INTRINSIC super-Poincar’e INEQUALITY RIEMANNIAN manifold diffusion SEMIGROUP 

分 类 号：O186.12[理学—数学]