Title
Eventual regularity of the volume-preserving mean curvature flow in 3D
Abstract
I will consider flat flow solutions for the volume-preserving mean curvature flow constructed via the minimizing movements scheme. It is known that in 3D, such flows converge (up to translation of the components) to a union of spheres, and when the flow converges to a single sphere, this convergence is exponential. I will present a regularity result showing that, in the latter case, the flow eventually becomes smooth and converges exponentially fast in C^k-norm, for all k, to the sphere. A key technical novelty of this work is that we prove regularity without relying on monotonicity formulas. This is a joint work with Vedansh Arya (Uppsala) and Seongmin Jeon (Seoul).
