Seminario del prof. Carlo Mantegazza - 11 giugno 2025

Giorno 11 giugno alle ore 15:00 in aula 124 il professore Carlo Mantegazza - Università di Napoli & Scuola Superiore Meridionale - terrà un seminario dal titolo:

Stability for the surface diffusion flow.

Abstract:
We study the surface diffusion flow in the flat torus, that is, smooth hypersurfaces moving with the outer normal velocity given by the Laplacian of their mean curvature. This model describes the evolution in time of interfaces between solid phases of a system, driven by the surface diffusion of atoms under the action of a chemical potential.
We show that if the initial set is sufficiently "close" to a strictly stable critical set for the Area functional under a volume constraint, then the flow actually exists for all times and asymptotically converges to a "translated" of the critical set. This generalizes the analogous result in dimension three, by Acerbi, Fusco, Julin and Morini.

Joint work with Antonia Diana e Nicola Fusco.