Preprint

Inserted: 29 sep 2026
Last Updated: 29 sep 2026

Year: 2026

Abstract:

We prove dynamical stability in arbitrary dimension for the modified Mullins--Sekerka flow, the gradient flow of the sharp-interface Ohta--Kawasaki energy on the flat torus. Specifically, we show that if an initial set has the same volume as a strictly stable critical set for the energy and is sufficiently close to it in $C^{3,\alpha}$, then the flow exists for all times and converges exponentially fast, in every $C^k$ norm, to a translate of that critical set. The proof relies on a quantitative Alexandrov-type estimate for strictly stable critical sets of the energy.

Tags: ANGEVA
, SiGmA

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