Paper · Dec 27, 2021
The Asymptotics of the Area-Preserving Mean Curvature and the Mullins-Sekerka Flow in Two Dimensions
As on arXiv
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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The asymptotic of the Mullins-Sekerka and the area-preserving curvature flow in the planar flat torus
Topics Volume-preserving & constrained flows · Shared terms “Mullins Sekerka”, “Sekerka flow”, “area preserving”
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Consistency of the flat flow solution to the volume preserving mean curvature flow
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Topics Volume-preserving & constrained flows · Same author Vesa Julin · Shared terms “flat flow”, “disjoint”, “perimeter”
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Topics Volume-preserving & constrained flows · Same author Vesa Julin · Shared terms “flat flow”
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Topics Volume-preserving & constrained flows · Shared terms “exponential”
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Topics Volume-preserving & constrained flows · Shared terms “area preserving”
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Nonlocal estimates for the Volume Preserving Mean Curvature Flow and applications
Topics Volume-preserving & constrained flows · Shared terms “asymptotics”
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Area-Preserving Anisotropic Mean Curvature Flow in Two Dimensions
Topics Volume-preserving & constrained flows · Shared terms “area preserving”, “flat flow”, “disjoint”
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Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.