Calculus of Variations and Geometric Measure Theory

V. Julin - M. Morini - M. Ponsiglione - E. Spadaro

The Asymptotics of the Area-Preserving Mean Curvature and the Mullins-Sekerka Flow in Two Dimensions

created by ponsiglio on 28 Dec 2021



Inserted: 28 dec 2021
Last Updated: 28 dec 2021

Year: 2021


We provide the first general result for the asymptotics of the area preserving mean curvature flow in two dimensions showing that flat flow solutions, starting from any bounded set of finite perimeter, converge with exponential rate to a finite union of equally sized disjoint disks. A similar result is established also for the periodic two-phase Mullins-Sekerka flow.