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arXiv · 2211.14257

Colding-Minicozzi Entropies in Cartan-Hadamard Manifolds

Jacob Bernstein·Arunima Bhattacharya
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Abstract

We introduce a family of functionals on submanifolds of Cartan-Hadamard manifolds that generalize the Colding-Minicozzi entropy of submanifolds of Euclidean space. We show that these functionals are monotone under mean curvature flow under natural conditions. As a consequence, we obtain sharp lower bounds on these entropies for certain closed hypersurfaces and observe a novel rigidity phenomenon.

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Jacob Bernstein, Arunima Bhattacharya. 2022-11-25. Colding-Minicozzi Entropies in Cartan-Hadamard Manifolds. https://arxiv.org/abs/2211.14257

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