  In this paper, we show that any embedded capillary hypersurface in the
half-space with anisotropic constant mean curvature is a truncated Wulff shape.
This extends Wente's result \cite{Wente80} to the anisotropic case and
He-Li-Ma-Ge's result \cite{HLMG09} to the capillary boundary case. The main
ingredients in the proof are a new Heintze-Karcher inequality and a new
Minkowski formula, which have their own inetrest.
