Published Paper

Inserted: 10 mar 2025
Last Updated: 8 oct 2025

Journal: J. Differ. Equ.
Year: 2025
Doi: https://doi.org/10.1016/j.jde.2025.113755

Abstract:

We study the asymptotic behavior of flat flow solutions to the periodic and planar two-phase Mullins-Sekerka flow and area-preserving curvature flow. We show that flat flows converge to either a finite union of equally sized disjoint disks or to a finite union of disjoint strips or to the complement of these configurations exponentially fast. A key ingredient in our approach is the derivation of a sharp quantitative Alexandrov inequality for periodic smooth sets.

Tags: ANGEVA