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f-Minimal Surface and Manifold with Positive m-Bakry–Émery Ricci Curvature

Li, Haizhong; Wei, Yong

Description

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...[Show more]

CollectionsANU Research Publications
Date published: 2015
Type: Journal article
URI: http://hdl.handle.net/1885/186627
Source: Journal of Geometric Analysis
DOI: 10.1007/s12220-013-9434-5

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