Hypersurface with capillary boundary evolving by the mean curvature

by Liangjun Weng (Università di Pisa)

Thursday 14 Mar 2024, 17:00 → 18:00 Europe/Rome

Aula Riunioni (Dipartimento di Matematica)

In this talk, we introduce a volume- or wetting area-preserving flow whose speed is given by the mean curvature with a non-local term for hypersurfaces with capillary boundary in the half-space. The non-local term creates additional difficulties, say for instance the comparison principle is no longer valid compared to locally constrained type flows. We demonstrate that for any convex initial hypersurface with a capillary boundary, the flow exists for all time and smoothly converges to a spherical cap as time goes to infinity.