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arXiv · 2112.13936

The Asymptotics of the Area-Preserving Mean Curvature and the Mullins-Sekerka Flow in Two Dimensions

Vesa Julin·Massimiliano Morini·Marcello Ponsiglione·Emanuele Spadaro
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Abstract

We provide the first general result for the asymptotics of the area preserving mean curvature flow in two dimensions showing that flat flow solutions, starting from any bounded set of finite perimeter, converge with exponential rate to a finite union of equally sized disjoint disks. A similar result is established also for the periodic two-phase Mullins-Sekerka flow.

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Vesa Julin, Massimiliano Morini, Marcello Ponsiglione, Emanuele Spadaro. 2021-12-27. The Asymptotics of the Area-Preserving Mean Curvature and the Mullins-Sekerka Flow in Two Dimensions. https://arxiv.org/abs/2112.13936

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