The mean curvature flow is an evolution of hypersurfaces satisfying a geometric heat equation. The flow naturally develops singularities so that it changes the topology of the hypersurfaces. There are infinitely many types of singularities, but it has been conjectured that the flow generically develops spherical or cylindrical singularities. Hence, it is important to show the well-posedness of the flow through cylindrical singularities. In this talk, we introduce the mean-convex neighborhood hood conjecture and its application to the well-posedness problem. If time permits, we discuss how to prove the conjecture by classifying ancient low entropy flows.

Kyeongsu Choi is a Professor in the School of Mathematics, Korea Institute for Advanced Study. He works on elliptic and parabolic PDEs and Geometric analysis. His research interests include singularity analysis for geometric flows. With his collaborators, he settled the mean convex neighborhood conjecture for the mean curvature flow to show the well-posedness around stable singularities. In addition, with other collaborators, he made contribution to the generic mean curvature flow by providing a way to avoid unstable singularities. 

He is also interested in fully nonlinear PDEs and free boundary problems. With other collaborators, he settled the Firey's conjecture for the Gauss curvature flow in all dimensions to investigate the asymptotic behavior of closed solutions.

Zoom Meeting ID：849 963 1368 
Passcode：YMSC