  We give a general criterion for the Dirichlet problem at infinity (DPI) on a
Cartan-Hadamard surface to be solvable, which we primarily use to give the best
possible upper radial radial curvature bound for solvability of the DPI, but
which is also flexible enough to accommodate flats. In particular, any (upper)
radial curvature bound which implies transience also implies solvability of the
DPI, which is perhaps surprising. Taking advantage of the structure provided by
uniformization, we show that solvability of the DPI implies there is a natural
continuous surjection of the Martin boundary onto the geometric boundary at
infinity. Finally, we give matched upper and lower radial curvature bounds that
imply the natural identification of the geometric and Martin boundaries (for
Cartan-Hadamard surfaces) that are more generous than the bounds that are known
in arbitrary dimension.
