  In this paper we investigate H-minimal graphs of lower regularity. We show
that noncharactersitic C^1 H-minimal graphs whose components of the unit
horizontal Gauss map are in W^{1,1} are ruled surfaces with C^2 seed curves. In
a different direction, we investigate ways in which patches of C^1 H-minimal
graphs can be glued together to form continuous piecewise C^1 H-minimal
surfaces.
  We apply these description of H-minimal graphs to the question of the
existence of smooth solutions to the Dirichlet problem with smooth data. We
find a necessary condition for the existence of smooth solutions and produce
examples where the conditions are satisfied and where they fail. In particular
we illustrate the failure of the smoothness of the data to force smoothness of
the solution to the Dirichlet problem by producing a class of smooth curves
whoses H-minimal spanning graphs cannot be C^2.
