  Gromov hyperbolic spaces have become an essential concept in geometry,
topology and group theory. Here we extend Ancona's potential theory on Gromov
hyperbolic manifolds and graphs of bounded geometry to a large class of
Schr\"odinger operators on Gromov hyperbolic metric measure spaces, unifying
these settings in a common framework ready for applications to singular spaces
such as RCD spaces or minimal hypersurfaces. Results include boundary Harnack
inequalities and a complete classification of positive harmonic functions in
terms of the Martin boundary which is identified with the geometric Gromov
boundary.
