Geometry & Topology Seminar: "Short-Time Existence of Mean Curvature Flow"

Abstract: Both Ricci and mean curvature flows, despite their formal analogy with heat flow, are given by PDE systems which are neither linear nor (strongly) parabolic. The underlying reason is the symmetry of these flows under reparametrization. As a result, the short-time existence of these flows can not be deduced directly from the standard parabolic theory.  Originally Hamilton applied his formulation of Nash-Moser implicit function theorem to establish the short-time existence of Ricci flow. Later DeTurck broke the symmetry mentioned above, and discovered an equivalent parabolic flow, hence the short-time existence. In this talk I will explain DeTurck's trick to construct short-time solution to mean curvature flow.

Host: Xiang Tang