Given an unbounded domain
of a Hadamard manifold
,
it makes sense to consider the problem of finding minimal graphs with
prescribed continuous data on its cone topology boundary, i.e., on its
ordinary boundary together with its asymptotic boundary. In this article
it is proved that under the hypothesis that the sectional curvature of
is
, this Dirichlet
problem is solvable if
satisfies a certain convexity condition at infinity and if
is mean convex. We also prove that mean convexity of
is a
necessary condition, extending to unbounded domains some results that are valid on
bounded ones.
Keywords
Dirichlet problem for minimal graphs, Hadamard manifolds
