Seminars & Colloquia Calendar

Abstract: We show that the mean curvature flow of generic closed surfaces in \(R^3\) avoids asymptotically conical and non-spherical compact singularities. We also show that the mean curvature flow of generic closed low-entropy hypersurfaces in \(R^4\) is smooth until it disappears in a round point. The main technical ingredient is a long-time existence and uniqueness result for ancient mean curvature flows that lie on one side of asymptotically conical or compact shrinking solitons. This is joint work with Otis Chodosh, Kyeongsu Choi and Christos Mantoulidis.

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