Title: Relation between singularity analysis and regularity theory of the Gauss curvature flow
Speaker: Kyeongsu Choi
Speaker Info: MIT
Brief Description:
Special Note:
Abstract:
We discuss evolution of closed convex hypersurfaces by powers p of their Gauss-Kronecker curvature. In the case p=1/(n+2), the flow converges to an ellipsoid after rescaling, which is related to the Affine Geometry. On the other hand, if p is in the range of [1/n,1/(n-1)], we can show that it converges to a sphere by using a technique of C^2 estimate for Monge-Ampere equations. To settle the higher case p>1/(n-1), we will study the optimal C^{1,p/(pn-1)} regularity and free boundary problems. Then, we can derive a geometric invariant which leads to the convergence to a sphere for all p>1/(n+2).Date: Monday, October 09, 2017