The asymptotic of the Mullins-Sekerka and the area-preserving curvature flow in the planar flat torus
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910866693160960 |
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| author | Arya, Vedansh De Gennaro, Daniele Kubin, Anna |
| author_facet | Arya, Vedansh De Gennaro, Daniele Kubin, Anna |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05399 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The asymptotic of the Mullins-Sekerka and the area-preserving curvature flow in the planar flat torus Arya, Vedansh De Gennaro, Daniele Kubin, Anna Differential Geometry Analysis of PDEs 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. |
| title | The asymptotic of the Mullins-Sekerka and the area-preserving curvature flow in the planar flat torus |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2503.05399 |