Sharp Entropy Bounds for Self-Shrinkers in Mean Curvature Flow

Abstract

Let $M\subset {\mathbf{R}}^{m+1}$ be a smooth, closed, codimension-one self-shrinker (for mean curvature flow) with nontrivial $k^{\mathrm{th}}$ homology. We show that the entropy of $M$ is greater than or equal to the entropy of a round $k$-sphere, and that if equality holds, then $M$ is a round $k$-sphere in ${\mathbf{R}}^{k+1}$.

7 pages. The new version (Oct 13, 2018) incorporates a few changes and clarifications suggested by the Geometry and Topology referees

References in corpus (1)

• Topology of Closed Hypersurfaces of Small Entropy

Cited by in corpus (2)

• Entropy Bounds, Compactness and Finiteness Theorems for Embedded Self-shrinkers with Rotational Symmetry
• On self shrinkers of medium entropy in ${\mathbb{R}}^4$