We construct geometric barriers for minimal graphs in H^n xR. We prove the
existence and uniqueness of a solution of the vertical minimal equation in the
interior of a convex polyhedron in H^n extending continuously to the interior
of each face, taking infinite boundary data on one face and zero boundary value
data on the other faces. In H^n xR, we solve the Dirichlet problem for the
vertical minimal equation in a C^0 convex domain taking arbitrarily continuous
finite boundary and asymptotic boundary data.