A Heintze-Karcher inequality with free boundaries and applications to capillarity theory
arXiv:2210.16376
Abstract
In this paper we analyze the shape of a droplet inside a smooth container. To characterize their shape in the capillarity regime, we obtain a new form of the Heintze-Karcher inequality for mean convex hypersurfaces with boundary lying on curved substrates.
31 pages, 3 figures, accepted version