Title: Uniqueness of stable capillary hypersurfaces in a ball,
Abstract: In this paper we prove that any immersed stable capillary hypersurfaces in a
ball in space forms are totally umbilical. This solves completely a
long-standing open problem. In the proof one of crucial ingredients is a new
Minkowski type formula. We also prove a Heintze-Karcher-Ros type inequality for
hypersurfaces in a ball, which, together with the new Minkowski formula, yields
a new proof of Alexandrov's Theorem for embedded CMC hypersurfaces in a ball
with free boundary.