  The aim of this article is the explicit construction of some barrier
functions ("fundamental solutions") for the Pucci-Heisenberg operators. Using
these functions we obtain the continuity property, up to the boundary, for the
viscosity solution of fully non-linear Dirichlet problems on the Heisenberg
group, if the boundary of the domain satisfies some regularity geometrical
assumptions (e.g. an exterior Heisenberg-ball condition at the characteristic
points). We point out that the knowledge of the fundamental solutions allows
also to obtain qualitative properties of Hadamard, Liouville and Harnack type.
