A characterization of the singular time of the mean curvature flow

Author:
Andrew A. Cooper

Journal:
Proc. Amer. Math. Soc. **139** (2011), 2933-2942

MSC (2010):
Primary 53C44

Published electronically:
January 3, 2011

MathSciNet review:
2801634

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Abstract | References | Similar Articles | Additional Information

Abstract: In this note we investigate the behaviour at finite-time singularities of the mean curvature flow of compact Riemannian submanifolds . We show that they are characterized by the blow-up of a trace of the square of the second fundamental form.

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Additional Information

**Andrew A. Cooper**

Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824

Email:
andrew.a.cooper@gmail.com

DOI:
http://dx.doi.org/10.1090/S0002-9939-2010-10714-1

Keywords:
Mean curvature flow

Received by editor(s):
February 24, 2009

Received by editor(s) in revised form:
July 31, 2009, February 16, 2010, and July 21, 2010

Published electronically:
January 3, 2011

Additional Notes:
The author was partially supported by RTG Research Training in Geometry and Topology NSF grant DMS 0353717 and as a graduate student by NSF grant DMS 06-04759.

Communicated by:
Richard A. Wentworth

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.