Geometry Seminar: R. Martin-Hagemeyer (UMass-Boston)

Geometry Seminar (Geometric Analysis)

Speaker: Rory Martin-Hagemeyer 

Title: On the Rate of Convergence of the Mean Curvature Flow

Abstract: We will prove that the rate of convergence of the rescaled mean curvature flow to a shrinker is at most exponential in the case of a compact initial hypersurface. We shall motivate and present the basic elements of the theory of mean curvature flow, starting with the basic elements of hypersurface geometry, shrinkers, rescaling of the mean curvature flow, and the convergence of the rescaled flow to a shrinker. Then we shall introduce a novel flow, the normal rescaled mean curvature flow, discuss its properties and compute some key evolution equations, and use it to establish our result.