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

Year: 2025

Type: preprint

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.

Source: arXiv (Cornell University)

Authors: Arya, Vedansh, De Gennaro, Daniele, Kubin, Anna

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6979242843

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