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 L2 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
Rimoldi, M. (2014). On a classification theorem for self–shrinkers. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 142(10), 3605-3613 [10.1090/S0002-9939-2014-12074-0].
On a classification theorem for self–shrinkers
RIMOLDI, MICHELE
2014
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 L2 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
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