Applications of Some Elliptic Equations in Riemannian Manifolds

Qin Huang; Qihua Ruan

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arXiv · 1301.1117

Applications of Some Elliptic Equations in Riemannian Manifolds

Qin Huang·Qihua Ruan

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Abstract

Let $(M^{n+1}, g)$ 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.

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BibTeX RIS

Qin Huang, Qihua Ruan. 2013-06-19. Applications of Some Elliptic Equations in Riemannian Manifolds. https://arxiv.org/abs/1301.1117

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