De Gennaro, D., Diana, A., Kubin, A., & Kubin, A. (2024). Stability of the surface diffusion flow and volume-preserving mean curvature flow in the flat torus. Mathematische Annalen, 390(3), 4429–4461. https://doi.org/10.1007/s00208-024-02863-3
We prove that, in the flat torus and in any dimension, the volume-preserving mean curvature flow and the surface diffusion flow, starting C1,1 -close to a strictly stable critical set of the perimeter E, exist for all times and converge to a translate of E exponentially fast as time goes to infinity.
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