Key points are not available for this paper at this time.
We prove a new Minkowski type formula for capillary hypersurfaces supported on totally geodesic hyperplanes in hyperbolic space. It leads to a volume-preserving flow starting from a star-shaped initial hypersurface. We prove the long-time existence of the flow and its uniform convergence to a -totally umbilical cap. Additionally, we establish that a -totally umbilical cap is an energy minimizer for a given enclosed volume.
Chai et al. (Sat,) studied this question.