Long-time behavior of volume preserving flows

Abstract

Using a suitable sharp quantitative Alexandrov estimate we show that the minimizing movements time discretization of the volume preserving mean curvature flow, starting from an arbitrary bounded set of finite perimeter, converges to a finite union of disjoint balls with exponential rate. We further show how to improve the estimate in two dimensions so as to obtain an analogous result for the limiting continuum flat flow.

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