  We prove that there exist solutions for a non-parametric capillary problem in
a wide class of Riemannian manifolds endowed with a Killing vector field. In
other terms, we prove the existence of Killing graphs with prescribed mean
curvature and prescribed contact angle along its boundary. These results may be
useful for modelling stationary hypersurfaces under the influence of a
non-homogeneous gravitational field defined over an arbitrary Riemannian
manifold.
