Geometric Analysis and Topology Seminar

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Colding-Minicozzi Entropies in Cartan-Hadamard Manifolds

Speaker: Jacob Bernstein, John Hopkins University

Location: Warren Weaver Hall 512

Date: Friday, December 2, 2022, 11 a.m.

Synopsis:

We discuss a new family of functionals on submanifolds of
Cartan-Hadamard manifolds that generalize the Colding-Minicozzi entropy
of submanifolds of Euclidean space. These quantities  are monotone
under mean curvature flow under natural conditions. As a consequence,
we obtain sharp lower bounds on them for certain closed hypersurfaces
and observe a novel rigidity phenomenon.  This is joint work with A.
Bhattacharya.