Applications of some elliptic equations in Riemannian manifolds

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:409

Article

Huang, Qin¹  Ruan, Qihua¹ 

[1] Putian Univ, Dept Math, Putian 351100, Fujian, Peoples R China

关键词: Riemannian manifold;    Bakry-Emery Ricci curvature;    Rigidity theorem;    Eigenvalue;    Weighted mean curvature;   

DOI  :  10.1016/j.jmaa.2013.07.004

来源: Elsevier

【 摘 要 】

Let (Mn+1, g) be a compact Riemannian manifold with smooth boundary B and nonnegative Bakry-Emery Ricci curvature. In this paper, we use the solvability of some elliptic equations to prove some estimates of the weighted mean curvature and some related rigidity theorems. As their applications, we obtain some lower bound estimate of the first nonzero eigenvalue of the drifting Laplacian acting on functions on B and some corresponding rigidity theorems. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free