Positive harmonic functions on abelian covers
The existence of positive harmonic functions and Green's functions on certain Abelian covers of non-compact, finite volume Riemann surfaces is shown. These results are obtained by studying the asymptotic distribution of the lattice in hyperbolic space generated by the fundamental group of the covering surface. They extend considerations by \textit{T.Lyons} and \textit{D. Sullivan} [J. Differ. Geom. 19, 299-323 (1984; Zbl 0554.58022)] on covers of compact Riemann surfaces using the theory of Brownian motion.
scientific article; zbMATH DE number 4122309
scientific article