Electronic International Standard Serial Number (EISSN)
1522-2616
abstract
We consider a planar Riemann surface R made of a non-compact simply connected plane domain from which an infinite discrete set of points is removed. We give several conditions for the collars of the cusps in R caused by these points to be uniformly distributed in R in terms of Euclidean geometry. Then we associate a graph G with R by taking the Voronoi diagram for the uniformly distributed cusps and show that G represents certain geometric and analytic properties of R. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim