  The work is motivated by a result of Manin, which relates the Arakelov Green
function on a compact Riemann surface to configurations of geodesics in a
3-dimensional hyperbolic handlebody with Schottky uniformization, having the
Riemann surface as conformal boundary at infinity. A natural question is to
what extent the result of Manin can be generalized to cases where, instead of
dealing with a single Riemann surface, one has several Riemann surfaces whose
union is the boundary of a hyperbolic 3-manifold, uniformized no longer by a
Schottky group, but by a Fuchsian, quasi-Fuchsian, or more general Kleinian
group. We have considered this question in this work and obtained several
partial results that contribute towards constructing an analog of Manin's
result in this more general context.
