Low Entropy and the Mean Curvature Flow with Surgery

2018/04/11 by Mramor, Alexander, Wang, Shengwen
#Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1804.04115

Abstract

In this article, we extend the mean curvature flow with surgery to mean convex hypersurfaces with entropy less than Λ_n-2. In particular, 2-convexity is not assumed. Next we show the surgery flow with just the initial convexity assumption H - (⟨ x, ν⟩)/(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 Λ_n-2 are isotopic to the round n-sphere.

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