Translators asymptotic to cylinders

2018/05/26 by Hershkovits, Or · 2 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.10553

Abstract

We show that the Bowl soliton in ℝ³ is the unique translating solutions of the mean curvature flow which has the family of shrinking cylinders as an asymptotic shrinker at -∞. As an application, we show that for a generic mean curvature flow, all (non-static) translating limit flows are the bowl soliton. The crucial point is that we do not make any global convexity assumption, while as the same time, the asymptotic requirement is very weak.

Cited by

• Mean curvature flow through singularities
• On steady and expanding Ricci solitons with asymptotic symmetries

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