Asian Journal of Mathematics
Volume 24 (2020)
Ricci-mean curvature flows in gradient shrinking Ricci solitons
Pages: 77 – 94
It was proved by Huisken that a mean curvature flow converges to a self-shrinker in the Euclidean space after scaling when it develops a singularity of type I. In this paper, we study a coupled flow with a mean curvature flow and a Ricci flow, and generalize his result for this Ricci-mean curvature flow. Then, as a parabolic rescaling limit, we get a self-shrinker in a gradient shrinking Ricci soliton in the sense of Lott under some assumptions.
mean curvature flow, Ricci flow, self-similar solution, gradient soliton
2010 Mathematics Subject Classification
This work was supported by Grant-in-Aid for JSPS Fellows Grant Number 13J06407, and by the Program for Leading Graduate Schools, MEXT, Japan.
Received 31 December 2016
Accepted 18 April 2019
Published 21 August 2020