Twists and Gromov hyperbolicity of riemann surfaces

Katsuhiko Matsuzaki, José M. Rodríguez

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4 Citations (Scopus)

Abstract

The main aim of this paper is to study whether the Gromov hyperbolicity is preserved under some transformations on Riemann surfaces (with their Poincaré metrics). We prove that quasiconformal maps between Riemann surfaces preserve hyperbolicity; however, we also show that arbitrary twists along simple closed geodesics do not preserve it, in general.

Original languageEnglish
Pages (from-to)29-44
Number of pages16
JournalActa Mathematica Sinica, English Series
Volume27
Issue number1
DOIs
Publication statusPublished - 2011 Jan 1

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Keywords

  • Gromov hyperbolicity
  • Quasiconformal maps
  • Riemann surfaces

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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