L-harmonic functions with polynomial growth of a fixed rate  

作　　者：ZHOU ChaoHui CHEN ZhiHua 

机构地区：[1]Department of Mathematics,Tongji University,Shanghai 200092,China

出　　处：《Science China Mathematics》2009年第12期2855-2862,共8页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.10571135)

摘　　要：Yau made the following conjecture:For a complete noncompact manifold with nonnegative Ricci curvature the space of harmonic functions with polynomial growth of a fixed rate is finite dimensional.we extend the result on the Laplace operator to that on the symmetric diffusion operator,and prove the space of L-harmonic functions with polynomial growth of a fixed rate is finitedimensional,when m-dimensional Bakery-Emery Ricci curvature of the symmetric diffusion operator on the complete noncompact Riemannian manifold is nonnegative.Yau made the following conjecture: For a complete noncompact manifold with nonnegative Ricci curvature the space of harmonic functions with polynomial growth of a fixed rate is finite dimensional. we extend the result on the Laplace operator to that on the symmetric diffusion operator, and prove the space of L-harmonic functions with polynomial growth of a fixed rate is finite-dimensional, when m-dimensional Bakery-Emery Ricci curvature of the symmetric diffusion operator on the complete noncompact Riemannian manifold is nonnegative.

关 键 词：L-harmonic function symmetric diffusion operator Bakery-Emery Ricci curvature 53C40 

分 类 号：O174.3[理学—数学]