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
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by Lu Wang

J. Amer. Math. Soc. 27 (2014), 613-638

DOI: https://doi.org/10.1090/S0894-0347-2014-00792-X

Published electronically: March 19, 2014

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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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