A Sharp Lower Bound for the Entropy of Closed Hypersurfaces up to Dimension Six
نویسندگان
چکیده
In [5], Colding-Ilmanen-Minicozzi-White showed that within the class of closed smooth self-shrinkers in R, the entropy is uniquely minimized at the round sphere. They conjectured that, for 2 ≤ n ≤ 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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