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arXiv · 1406.2966

A Sharp Lower Bound for the Entropy of Closed Hypersurfaces up to Dimension Six

Jacob Bernstein·Lu Wang
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Abstract

In [5], Colding-Ilmanen-Minicozzi-White showed that within the class of closed smooth self-shrinkers in $\mathbb{R}^{n+1}$, the entropy is uniquely minimized at the round sphere. They conjectured that, for $2\leq n\leq 6$, the round sphere minimizes the entropy among all closed smooth hypersurfaces. Using an appropriate weak mean curvature flow, we prove their conjecture. For these dimensions, our approach also gives a new proof of the main result of [5] and extends its conclusions to compact singular self-shrinkers.

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Jacob Bernstein, Lu Wang. 2014-06-11. A Sharp Lower Bound for the Entropy of Closed Hypersurfaces up to Dimension Six. https://arxiv.org/abs/1406.2966

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