Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

Request Permissions   Purchase Content 
 

 

On a classification theorem for self-shrinkers


Author: Michele Rimoldi
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
Published electronically: June 12, 2014
MathSciNet review: 3238436
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 53C44, 53C21

Retrieve articles in all journals with MSC (2010): 53C44, 53C21


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

DOI: https://doi.org/10.1090/S0002-9939-2014-12074-0
Keywords: Self--shrinkers, classification, weighted manifolds
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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.