Uniqueness of Self-similar Shrinkers with Asymptotically Conical Ends

By Lu Wang. 2011

71 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1fc101d556cb4fa78e8569ccb12729cb5a3828e2

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Uniqueness of the bowl soliton (2014, methodology): “A very important contribution was made by X. Wang [Wan11], who proved that for n = 2 any entire convex solution must be the rotationally symmetric bowl soliton, but that for n ≥ 3 there exist entire strictly convex solution that are not rotationally symmetric.”
Embedded self-similar shrinkers of genus 0 (2014, background): “We note that L. Wang [23] has obtained a classiﬁcation of self-similar shrinkers which are asymptotic to cones.”
Uniqueness of asymptotically conical tangent flows (2019, background): “osed hypersurface (up to the singular dimension, cf. [Zhu16] and see also [CIMW13, KZ18]); the same authors have extended [BW17b] this to noncompact surfaces in R3 (see also [BW18b]). Wang has proven [Wan14] that two shrinkers asymptotic to the same smooth cone must be identical. Ketover has recentl”
Rigidity of asymptotically conical shrinking gradient Ricci solitons (2013, methodology): “2 of [52] to time-dependent backwardheat operators acting on sections of tensor bundles.”