Prescribing Curvature Problems on the Bakry-Emery Ricci Tensor of a Compact Manifold with Boundary  

作　　者：Weimin SHENG Lixia YUAN 

机构地区：[1]Department of Mathematics,Zhejiang University [2]Department of Mathematics,Xinjiang Normal University

出　　处：《Chinese Annals of Mathematics,Series B》2014年第1期139-160,共22页数学年刊（B辑英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.10831008,11131007)

摘　　要：t The authors consider the problem of conformally deforming a metric such that the k-curvature defined by an elementary symmetric function of the eigenvalues of the Bakry-Emery Ricci tensor on a compact manifold with boundary to a prescribed function. A consequence of our main result is that there exists a complete metric such that the Monge-Amp^re type equation with respect to its Bakry-Emery Ricci tensor is solvable, provided that the initial Bakry-Emery Ricci tensor belongs to a negative convex cone.

关 键 词：k-Curvature Bakry-Emery Ricci tensor Complete metric Dirichletproblem 

分 类 号：O186.12[理学—数学]