Speaker：LIN Longzhi (UC Santa Cruz)

Time: 2016-07-08， 15:00-16:00

Place：Room 1518, School of Mathematical Sciences 

Detail: A one-parameter family of hypersurfaces in Euclidean space evolves by mean curvature flow (MCF) if the velocity at each point is given by the mean curvature vector. It can be viewed as a geometric heat equation, i.e., it is locally moving in the direction of steepest descent for the volume element, deforming surfaces towards optimal ones (minimal surfaces). In this talk we will discuss some recent work on the local curvature estimate and convexity estimate for the star-shaped MCF and the consequences. These estimates hold for any singularities via elliptic regularization. In particular, star-shaped MCFs have only convex limit flows and therefore are generic in the sense of Colding-Minicozzi.

Organizer: School of Mathematical Sciences