Planar Riemann surfaces with uniformly distributed cusps: parabolicity and hyperbolicity

Katsuhiko Matsuzaki, José M. Rodríguez

    Research output: Contribution to journalArticle

    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 languageEnglish
    Pages (from-to)1097-1112
    Number of pages16
    JournalMathematische Nachrichten
    Volume290
    Issue number7
    DOIs
    Publication statusPublished - 2017 May 1

    Fingerprint

    Hyperbolicity
    Cusp
    Riemann Surface
    Euclidean geometry
    Voronoi Diagram
    Set of points
    Graph in graph theory

    Keywords

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

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Planar Riemann surfaces with uniformly distributed cusps : parabolicity and hyperbolicity. / Matsuzaki, Katsuhiko; Rodríguez, José M.

    In: Mathematische Nachrichten, Vol. 290, No. 7, 01.05.2017, p. 1097-1112.

    Research output: Contribution to journalArticle

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