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Uniqueness of self-similar shrinkers with asymptotically conical ends


Author: Lu Wang
Journal: J. Amer. Math. Soc. 27 (2014), 613-638
MSC (2010): Primary 53C44, 53C24, 35J15; Secondary 35B60
DOI: https://doi.org/10.1090/S0894-0347-2014-00792-X
Published electronically: March 19, 2014
MathSciNet review: 3194490
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Abstract: Let $ C\subset \mathbb{R}^{n+1}$ be a regular cone with vertex at the origin. In this paper, we show the uniqueness for smooth properly embedded self-shrinking ends in $ \mathbb{R}^{n+1}$ that are asymptotic to $ C$. As an application, we prove that not every regular cone with vertex at the origin has a smooth complete properly embedded self-shrinker asymptotic to it.


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Additional Information

Lu Wang
Affiliation: Department of Mathematics, Johns Hopkins University, 3400 N. Charles Street, Baltimore, Maryland 21218
Email: coral0426@gmail.com

DOI: https://doi.org/10.1090/S0894-0347-2014-00792-X
Keywords: Self-shrinkers, mean curvature flow, backwards uniqueness
Received by editor(s): October 3, 2011
Received by editor(s) in revised form: June 27, 2013, and October 19, 2013
Published electronically: March 19, 2014
Article copyright: © Copyright 2014 American Mathematical Society