Star-Shaped Mean Curvature Seminar - Longzhi Lin (UC Santa Cruz)

Event Date: 

Friday, May 8, 2015 -
3:00pm to 4:00pm

Event Location: 

  • 6635 South Hall

Event Price: 

Free

Event Contact: 

Lee Kennard
Email: kennard@math.ucsb.edu
 
  • Differential Geometry Seminar

A one-parameter family of hypersurfaces in Euclidean space evolves by mean curvature flow 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 mean curvature flow and the consequences. In particular, star-shaped MCF is generic in the sense of Colding-Minicozzi. This is joint work with Robert Haslhofer.