Arya, V., De Gennaro, D., & Kubin, A. (2026). The asymptotic of the Mullins-Sekerka and the area-preserving curvature flow in the planar flat torus. Journal of Differential Equations, 451, Article 113755. https://doi.org/10.1016/j.jde.2025.113755
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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Project title:
Quantum Optical Binding of Levitated Nanoparticles QBind Application for the Principal Investigator Project Submitted to the Austrian Science Fund (FWF) by Dr. Uros: PAT8785024 (FWF - Österr. Wissenschaftsfonds)
