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

2021/12/27 by Julin, Vesa, Morini, Massimiliano, Ponsiglione, Marcello +1 · 4 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.13936

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.

Cited by

• Flat flows of periodic Lipschitz subgraphs for generalized nonlocal perimeters
• Existence of flat flows for volume-preserving mean curvature flow with contact angle
• Quantitative estimates for the relative isoperimetric problem and its gradient flow outside convex bodies in the plane
• A variational approach to the volume-preserving anisotropic mean curvature flow in 2D

Related

• The asymptotic of the Mullins-Sekerka and the area-preserving curvature flow in the planar flat torus
• Asymptotic behavior of a diffused interface volume-preserving mean curvature flow
• Stability of the surface area preserving mean curvature flow in Euclidean space
• Area-Preserving Anisotropic Mean Curvature Flow in Two Dimensions
• Stability of the area preserving mean curvature flow in asymptotic Schwarzschild space