Uniqueness of self-similar shrinkers with asymptotically conical ends

Wang, Lu

doi:10.1090/S0894-0347-2014-00792-X

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 | References | Similar Articles | Additional Information

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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