Stability of the surface diffusion flow and volume-preserving mean curvature flow in the flat torus
Abstract
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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