Planar Riemann surfaces with uniformly distributed cusps: parabolicity and hyperbolicity

Katsuhiko Matsuzaki; José M. Rodríguez

doi:10.1002/mana.201400241

Planar Riemann surfaces with uniformly distributed cusps: parabolicity and hyperbolicity

Katsuhiko Matsuzaki, José M. Rodríguez^*

^*Corresponding author for this work

School of Education

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1097-1112
Number of pages	16
Journal	Mathematische Nachrichten
Volume	290
Issue number	7
DOIs	https://doi.org/10.1002/mana.201400241
Publication status	Published - 2017 May

Keywords

Green's function
Gromov hyperbolic
Poincaré metric
Voronoi diagram
linear isoperimetric inequality
quasi-isometry

ASJC Scopus subject areas

Mathematics(all)

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10.1002/mana.201400241

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title = "Planar Riemann surfaces with uniformly distributed cusps: parabolicity and hyperbolicity",

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.",

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author = "Katsuhiko Matsuzaki and Rodr{\'i}guez, {Jos{\'e} M.}",

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T1 - Planar Riemann surfaces with uniformly distributed cusps

T2 - parabolicity and hyperbolicity

AU - Matsuzaki, Katsuhiko

AU - Rodríguez, José M.

PY - 2017/5

Y1 - 2017/5

N2 - 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.

AB - 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.

KW - Green's function

KW - Gromov hyperbolic

KW - Poincaré metric

KW - Voronoi diagram

KW - linear isoperimetric inequality

KW - quasi-isometry

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DO - 10.1002/mana.201400241

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AN - SCOPUS:85018951914

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VL - 290

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JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

IS - 7

ER -

Planar Riemann surfaces with uniformly distributed cusps: parabolicity and hyperbolicity

Abstract

Keywords

ASJC Scopus subject areas

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