Calculus of Variations and Geometric Measure Theory

A. Mramor - S. Wang

Low Entropy and the Mean Curvature Flow with Surgery

created by wang on 13 Nov 2020



Inserted: 13 nov 2020

Year: 2018

ArXiv: 1804.04115 PDF


In this article, we extend the mean curvature flow with surgery to mean convex hypersurfaces with entropy less than $\Lambda_{n-2}$. In particular, 2-convexity is not assumed. Next we show the surgery flow with just the initial convexity assumption $H - \frac{\langle x, \nu \rangle}{2} > 0$ is possible and as an application we use the surgery flow to show that smooth $n$-dimensional closed self shrinkers with entropy less than $\Lambda_{n-2}$ are isotopic to the round $n$-sphere.