THE RELATION BETWEEN ARAKELOV GREEN’S FUNCTIONS OF THE BOUNDARIES AT INFINITY OF THE HYPERBOLIC 3-MANIFOLDS

Suppose that M is a hyperbolic 3-Manifold with infinite volume and having compact Riemann surfaces S1; S2; :::; Sn+1 as its conformal boundaries at infinity. Also choose a geometry on M which bears a metric of constant negative curvature. Then we can define Arakelov Green’s functions on each Si with respect to this metric and a divisor. In this paper we try to find a relation between the Green’s functions associated to each component Si.