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arXiv · 1803.00637

Sharp Entropy Bounds for Self-Shrinkers in Mean Curvature Flow

Or Hershkovits·Brian White
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Abstract

Let $M\subset {\mathbf R}^{m+1}$ be a smooth, closed, codimension-one self-shrinker (for mean curvature flow) with nontrivial $k^{\rm th}$ 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 ${\mathbf R}^{k+1}$.

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Or Hershkovits, Brian White. 2018-10-14. Sharp Entropy Bounds for Self-Shrinkers in Mean Curvature Flow. https://doi.org/10.2140/gt.2019.23.1611

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