f-Minimal Surface and Manifold with Positive m-Bakry–émery Ricci Curvature
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- 作者：Haizhong Li ; Yong Wei
- 关键词：f ; Mean curvature ; f ; Minimal ; m ; Bakry–émery Ricci curvature ; Eigenvalue estimate ; 53C42 ; 53C21
- 刊名：Journal of Geometric Analysis
- 出版年：2015
- 出版时间：January 2015
- 年：2015
- 卷：25
- 期：1
- 页码：421-435
- 全文大小：339 KB
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文摘
In this paper, we first prove a compactness theorem for the space of closed embedded f-minimal surfaces of fixed topology in a closed three-manifold with positive Bakry–émery Ricci curvature. Then we give a Lichnerowicz type lower bound of the first eigenvalue of the f-Laplacian on a compact manifold with positive m-Bakry–émery Ricci curvature, and prove that the lower bound is achieved only if the manifold is isometric to the n-sphere, or the n-dimensional hemisphere. Finally, for a compact manifold with positive m-Bakry–émery Ricci curvature and f-mean convex boundary, we prove an upper bound for the distance function to the boundary, and the upper bound is achieved if and only if the manifold is isometric to a Euclidean ball.