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Local Regularity in Mean Curvature Flow

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I will introduce the notion of a mean curvature flow (in the classical smooth setting) before going on to discuss the much celebrated local regularity theorem of Brian White and some of its consequences. This local regularity theorem is something like a parabolic analogue of Allard’s regularity theorem, and applies to a wide class of flows, in particular to certain `weak’ flows arising as measure theoretic limits of smooth flows. Time permitting I will then also describe its application to current joint work with Kim Moore on a short time existence theorem for Lagrangian mean curvature flow with non-smooth initial data (specifically initial data with singularities asymptotic to a transversally intersecting pair of planes).

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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