Stability of the volume preserving mean curvature flow in the flat torus

Mathphys Analysis Seminar

In this talk, we analyse the exponential stability for the volume preserving mean curvature flow in the flat torus. More precisely, we show that the flow starting near a strictly stable critical set E of the perimeter converges in the long time to a translation of E exponentially fast. We prove this result both for the classical case and for the time-discrete case (Almgren-Taylor-Wang scheme).
An important tool of these proof consists in a new quantitative estimate of Alexandrov type for constant mean curvature hypersurfaces. These works have been done in collaboration with D. De Gennaro, A. Dianaand A. Kubin