Applications of some elliptic equations in Riemannian manifolds

作者：Huang Qin; Ruan Qihua^*

来源：Journal of Mathematical Analysis and Applications, 2014, 409(1): 189-196.

DOI：10.1016/j.jmaa.2013.07.004

• Riemannian manifold
• Bakry-Emery Ricci curvature
• Rigidity theorem
• Eigenvalue
• Weighted mean curvature

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.

• 出版日期2014-1-1
• 单位莆田学院