Colding-Minicozzi entropies in Cartan-Hadamard manifolds

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Jacob Bernstein, Johns Hopkins University

I will discuss a family of functionals defined on submanifolds of听Cartan-Hadamard manifolds that generalize the Colding-Minicozzi entropy听of submanifolds of Euclidean space. These quantities are monotone听under mean curvature flow under natural conditions. As a consequence,听we obtain sharp lower bounds on them for certain closed hypersurfaces听and observe a novel rigidity phenomenon.听

This is joint work with A.听Bhattacharya.