  In this paper, we establish a Heintze-Karcher-type inequality for capillary
hypersurfaces in a unit ball. To achieve this, we introduce a special Finsler
metric given by Zermelo's navigation and study the geodesic normal flow with
respect to this Finsler metric. Our results indicate that the relationship
between capillary hypersufaces and hypersurfaces with free boundary is similar
to the one between Finsler geometry and Riemannian geometry.
