Abstract

The work is motivated by a result of Manin in [1], which relates the Arakelov Green’s   function on a compact Riemann surface to configurations of geodesics in a 3-dimensional hyperbolic handlebody with Schottky uniformization, having the Riemann surface as a   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.