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arXiv · 2503.05399

The asymptotic of the Mullins-Sekerka and the area-preserving curvature flow in the planar flat torus

Vedansh Arya·Daniele De Gennaro·Anna Kubin
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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.

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Vedansh Arya, Daniele De Gennaro, Anna Kubin. 2025-03-07. The asymptotic of the Mullins-Sekerka and the area-preserving curvature flow in the planar flat torus. https://arxiv.org/abs/2503.05399

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