Volume preserving mean curvature flows near strictly stable sets in flat torus

2019/07/08 by Niinikoski, Joonas · 1 citation
#53C44 (Primary) and 35K93 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.03618

Abstract

In this paper we establish a new stability result for the smooth volume preserving mean curvature flow in flat torus \mathbb Tⁿ in low dimensions n=3,4. The result says roughly that if the initial set is near to a strictly stable set in \mathbb Tⁿ in H³-sense, then the corresponding flow has infinite lifetime and converges exponentially fast to a translate of the strictly stable (critical) set in W^2,5-sense.

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• A variational approach to the volume-preserving anisotropic mean curvature flow in 2D

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