Uniqueness of self-similar shrinkers with asymptotically conical ends

Wang, Lu ¹

¹ Department of Mathematics, Johns Hopkins University, 3400 N. Charles Street, Baltimore, Maryland 21218

Journal of the American Mathematical Society, Tome 27 (2014) no. 3, pp. 613-638

Résumé

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.

Détail

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

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