A characterization of the singular time of the mean curvature flow
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- by Andrew A. Cooper PDF
- Proc. Amer. Math. Soc. 139 (2011), 2933-2942 Request permission
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.References
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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
- 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
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 2933-2942
- MSC (2000): Primary 53C44
- DOI: https://doi.org/10.1090/S0002-9939-2010-10714-1
- MathSciNet review: 2801634