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Uniqueness of Self-similar Shrinkers with Asymptotically Conical Ends (1110.0450v1)
Published 3 Oct 2011 in math.DG and math.AP
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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