Speaker: Alexander Mramor (University of Oklahoma)

Title: On the long-term behavior of the mean curvature flow in 3-manifolds

Abstract:

In this talk I’ll discuss recent joint work with Ao Sun where we consider the fate of the mean curvature flow in closed 3-manifolds. Employing many important recent advances on the mean curvature flow we can show that almost regular flows, as introduced by Bamler and Kleiner, will either go extinct in finite time or converge, possibly with multiplicity, to a minimal surface; by a perturbation argument one can go on to construct piecewise almost regular flows where the limit, if nonempty, must be stable. Using this we can use the flow to construct minimal surfaces in 3-manifolds in a variety of circumstances, mainly novel from the point of view that the arguments are via parabolic methods.