Analysis Seminar

Hypersurface with capillary boundary evolving by the mean curvature

by Liangjun Weng (Università di Pisa)

Aula Riunioni (Dipartimento di Matematica)

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 The non-local term creates additional difficulties, say for instance the comparison principle is no longer valid compared to locally constrained type flows.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.