BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Felix Schulze (University of Warwick) DTSTART:20210921T170000Z DTEND:20210921T180000Z DTSTAMP:20260423T035020Z UID:OSGA/80 DESCRIPTION:Title: Me an curvature flow with generic initial data\nby Felix Schulze (Univers ity of Warwick) as part of Online Seminar "Geometric Analysis"\n\n\nAbstra ct\nMean curvature flow is the gradient flow of the area functional and co nstitutes a natural geometric heat equation on the space of hypersurfaces in an ambient Riemannian manifold. It is believed\, similar to Ricci Flow in the intrinsic setting\, to have the potential to serve as a tool to app roach several fundamental conjectures in geometry. The obstacle for these applications is that the flow develops singularities\, which one in genera l might not be able to classify completely. Nevertheless\, a well-known co njecture of Huisken states that a generic mean curvature flow should have only spherical and cylindrical singularities. As a first step in this dire ction Colding-Minicozzi have shown in fundamental work that spheres and cy linders are the only linearly stable singularity models. As a second step toward Huisken's conjecture we show that mean curvature flow of generic in itial closed surfaces in $\\mathbb{R}^3$ avoids asymptotically conical and non-spherical compact singularities. The main technical ingredient is a l ong-time existence and uniqueness result for ancient mean curvature flows that lie on one side of asymptotically conical or compact self-similarly s hrinking solutions. This is joint work with Otis Chodosh\, Kyeongsu Choi a nd Christos Mantoulidis.\n LOCATION:https://researchseminars.org/talk/OSGA/80/ END:VEVENT END:VCALENDAR