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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On a classification theorem for self–shrinkers
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by Michele Rimoldi PDF
Proc. Amer. Math. Soc. 142 (2014), 3605-3613 Request permission


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.
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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:
  • 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:
  • MathSciNet review: 3238436