Uniqueness of Self-similar Shrinkers with Asymptotically Conical Ends

Mathematics – Differential Geometry

Scientific paper

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24 pages, 0 figures

Scientific paper

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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