On a classification theorem for self–shrinkers
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- by Michele Rimoldi PDF
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Abstract:
We generalize a classification result for self–shrinkers of the mean curvature flow with nonnegative mean curvature, which was obtained by Colding and Minicozzi, by replacing the assumption on polynomial volume growth with a weighted $L^2$ condition on the norm of the second fundamental form. Our approach adopts the viewpoint of weighted manifolds and also permits us to recover and to extend some other recent classification and gap results for self–shrinkers.References
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Additional Information
- Michele Rimoldi
- Affiliation: Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell’Insubria, via Valleggio 11, I-22100 Como, Italy
- Address at time of publication: Dipartimento di Matematica e Applicazioni, Universitá degli Studi di Milano-Bicocca, via Cozzi, 55, I-20125 Milano, Italy
- Email: michele.rimoldi@gmail.com
- Received by editor(s): July 10, 2012
- Received by editor(s) in revised form: October 17, 2012
- Published electronically: June 12, 2014
- Communicated by: Lei Ni
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 3605-3613
- MSC (2010): Primary 53C44, 53C21
- DOI: https://doi.org/10.1090/S0002-9939-2014-12074-0
- MathSciNet review: 3238436