Entropy in mean curvature flow

Abstract

The entropy of a hypersurface is defined by the supremum over all Gaussian integrals with varying centers and scales, thus invariant under rigid motions and dilations. It measures geometric complexity and is motivated by the study of mean curvature flow. We will survey recent progress on conjectures of Colding–Ilmanen–Minicozzi–White concerning the sharp lower bound on entropy for hypersurfaces, as well as their extensions.