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arXiv · 2407.02332

Li-Yau Conformal Volume and Colding-Minicozzi Entropy of Self-Shrinkers

Jacob Bernstein
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Abstract

We show the (normalized) Li-Yau conformal volume of a self-shrinker of mean curvature flow in Euclidean space bounds its Colding-Minicozzi entropy from below. This bound is independent of codimension and sharp on planes. As an application we verify a conjecture of Colding-Minicozzi about the entropy of closed self-shrinkers of arbitrary codimension for self-shrinkers that are topologically two-dimensional real projective planes. As part of the proof we introduce two auxiliary functionals which we call stable conformal volume and virtual entropy which should be of independent interest.

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Jacob Bernstein. 2024-07-02. Li-Yau Conformal Volume and Colding-Minicozzi Entropy of Self-Shrinkers. https://arxiv.org/abs/2407.02332

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