Positive harmonic functions on abelian covers (Q1825995)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Positive harmonic functions on abelian covers |
scientific article; zbMATH DE number 4122309
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Positive harmonic functions on abelian covers |
scientific article; zbMATH DE number 4122309 |
Statements
Positive harmonic functions on abelian covers (English)
0 references
1989
0 references
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.
0 references
Green's functions
0 references
hyperbolic space
0 references
positive harmonic functions
0 references
lattice
0 references
0 references
