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The self-shrinker in warped product space and the weighted Minkowski inequality


Author: Guoqiang Wu
Journal: Proc. Amer. Math. Soc. 145 (2017), 1763-1772
MSC (2010): Primary 53C44; Secondary 53C24
DOI: https://doi.org/10.1090/proc/13325
Published electronically: October 18, 2016
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Abstract: This paper consists of two parts. One is that for a kind of self-shrinker in a manifold with warped product metric, we prove that under some conditions on ambient space, the mean convex self-shrinker must have parallel second fundamental form. The other one is a generalization of Brendle's Minkowski inequality for weighted mean curvature.


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Guoqiang Wu
Affiliation: Department of Mathematics, East China Normal University, Shanghai 200000, People’s Republic of China
Email: gqwu@math.ecnu.edu.cn

DOI: https://doi.org/10.1090/proc/13325
Keywords: Self-shrinker, warped product, Minkowski inequality
Received by editor(s): March 1, 2016
Received by editor(s) in revised form: June 3, 2016
Published electronically: October 18, 2016
Communicated by: Lei Ni
Article copyright: © Copyright 2016 American Mathematical Society