Mean curvature flow with generic initial data II

2023/02/16 by Otis Chodosh, Kyeongsu Choi, Chodosh, Otis +3 · 3 citations
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Black Holes and Theoretical Physics

paper · pdf · doi:10.48550/arxiv.2302.08409

Abstract

We show that the mean curvature flow of a generic closed surface in ℝ³ avoids multiplicity one tangent flows that are not round spheres/cylinders. In particular, we show that any non-cylindrical self-shrinker with a cylindrical end cannot arise generically.

Cited by

• Linear stability and instability of Kähler Ricci solitons
• Mean curvature flow through singularities
• Self-expanders of positive genus

Related

• Generic mean curvature flow I; generic singularities
• Mean curvature flow with generic initial data
• Local Entropy and Generic Multiplicity One Singularities of Mean Curvature Flow of Surfaces
• Revisiting generic mean curvature flow in ℝ³
• General curvature flow without singularities