Ricci-mean curvature flows in gradient shrinking Ricci solitons

2015/01/26 by Yamamoto, Hikaru · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1501.06256

Abstract

Huisken studied asymptotic behavior of a mean curvature flow in a Euclidean space when it develops a singularity of type I, and proved that its rescaled flow converges to a self-shrinker in the Euclidean space. In this paper, we generalize this result for a Ricci-mean curvature flow moving along a Ricci flow constructed from a gradient shrinking Ricci soliton.

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• Mean curvature flow into an ambient Riemannian manifold evolving by Ricci flow coupled with harmonic map heat flow

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