Event
Classifications of ancient mean curvature flows| Title of the event | Classifications of ancient mean curvature flows |
| Series | SonstigeVeranstaltungenMI |
| Organizer | Fakultät für Mathematik und Informatik |
| Speaker | Niels Martin Møller |
| Speaker institution | University of Copenhagen |
| Type of event | Vortrag |
| Category | Forschung |
| Registration required | Nein |
| Details | 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. 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 flows, with ties to some classical open problems about minimal hypersurfaces in higher dimensions. The proofs use a new parabolic Omori-Yau maximum principle for proper ancient flows. This is joint work with Francesco Chini. |
| Date | Start: 26.10.2020, 16:15 Uhr Ende: 26.10.2020 , 17:30 Uhr |
| Location |
Mathematisches Institut (Bunsenstr 3-5) Maximum plus Streaming |
| Contact |
0551/39-27752 linda.cassel@mathematik.uni-goettingen.de |