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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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: In this note we investigate the behaviour at finite-time singularities of the mean curvature flow of compact Riemannian submanifolds $ M_t^m\hookrightarrow (N^{m+n},h)$. We show that they are characterized by the blow-up of a trace $ A=H\cdot\operatorname{II}$ 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
PII: S 0002-9939(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.