TY - JOUR
T1 - Twists and Gromov hyperbolicity of riemann surfaces
AU - Matsuzaki, Katsuhiko
AU - Rodríguez, José M.
N1 - Funding Information:
Received November 20, 2009, accepted June 13, 2010 The second author is supported in part by two grants from Ministerio de Ciencia e Innovación (MTM 2009-07800 and MTM 2008-02829-E), Spain
PY - 2011/1
Y1 - 2011/1
N2 - 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.
AB - 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.
KW - Gromov hyperbolicity
KW - Quasiconformal maps
KW - Riemann surfaces
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U2 - 10.1007/s10114-011-9693-7
DO - 10.1007/s10114-011-9693-7
M3 - Article
AN - SCOPUS:78650360635
SN - 1439-8516
VL - 27
SP - 29
EP - 44
JO - Acta Mathematica Sinica, English Series
JF - Acta Mathematica Sinica, English Series
IS - 1
ER -