Classifications of ancient mean curvature flows
speaker: Niels Martin Møller (University of Copenhagen)abstract: We show that a "wedge theorem" holds for all properly immersed ancient solutions to the mean curvature flow in \mathbb{R}{n+1}. This nonlinear parabolic Liouville-type result adds to a long story, as it generalizes the wedge theorem for self-translaters (minimal surfaces in a certain conformally flat space) from 2018, which in turn implies the minimal surface case by Hoffman-Meeks (1990) that again contains the classical cone case by Omori (1967). An application is to classify the convex hulls of the sets of reach of all proper ancient flows, without any of the usual curvature assumptions. This gives new obstructions to the possible singularities that can occur in mean curvature flow. The proofs use a parabolic Omori-Yau maximum principle for proper ancient flows. This is joint work with Francesco Chini (U Copenhagen).
timetable:
Wed 27 Nov, 9:15 - 10:05, Aula Dini
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