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

Wu, Guoqiang

doi:10.1090/proc/13325

The self-shrinker in warped product space and the weighted Minkowski inequality
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Proc. Amer. Math. Soc. 145 (2017), 1763-1772 Request permission

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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