Communications in Analysis and Geometry

Volume 26 (2018)

Number 5

Asymptotic behavior of Type III mean curvature flow on noncompact hypersurfaces

Pages: 1079 – 1101

DOI: https://dx.doi.org/10.4310/CAG.2018.v26.n5.a3

Authors

Liang Cheng (School of Mathematics and Statistics, Huazhong Normal University, Wuhan, China)

Natasa Sesum (Department of Mathematics, Rutgers University, Piscataway, New Jersey, U.S.A.)

Abstract

In this paper, we introduce the monotonicity formulas for the mean curvature flow which are related to self-expanders. Then we use the monotonicity to study the asymptotic behavior of Type III mean curvature flow on noncompact hypersurfaces.

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Liang Cheng’s Research partially supported by the Natural Science Foundation of China 11571131, a scholarship from the China Scholarship Council and the Fundamental Research Funds for the Central Universities, CCNU16A02010. Natasa Sesum thanks the NSF support in DMS-0905749 and DMS-1056387.

Received 29 April 2015

Published 3 January 2019