Communications in Analysis and Geometry

Volume 21 (2013)

Number 3

Mean curvature flow of higher codimension in hyperbolic spaces

Pages: 651 – 669

DOI: https://dx.doi.org/10.4310/CAG.2013.v21.n3.a8

Authors

Kefeng Liu (Department of Mathematics, University of California at Los Angeles)

Hongwei Xu (Center of Mathematical Sciences, Zhejiang University, Hangzhou, China)

Fei Ye (Center of Mathematical Sciences, Zhejiang University, Hangzhou, China)

Entao Zhao (Center of Mathematical Sciences, Zhejiang University, Hangzhou, China)

Abstract

In this paper, we investigate the convergence for the mean curvature flow of closed submanifolds with arbitrary codimension in space forms. Particularly, we prove that the mean curvature flow deforms a closed submanifold satisfying a pinching condition in a hyperbolic space form to a round point in finite time.

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Published 5 July 2013