Planar Riemann surfaces with uniformly distributed cusps: parabolicity and hyperbolicity | Zendy

Matsuzaki Katsuhiko | Zendy; Rodríguez José M. | Zendy

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Planar Riemann surfaces with uniformly distributed cusps: parabolicity and hyperbolicity

Author(s) -

Matsuzaki Katsuhiko,

Rodríguez José M.

Publication year - 2017

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.201400241

Subject(s) - mathematics , riemann surface , planar , voronoi diagram , euclidean geometry , simply connected space , plane (geometry) , graph , planar graph , surface (topology) , riemann hypothesis , mathematical analysis , geometry , pure mathematics , combinatorics , computer graphics (images) , computer science

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 .

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