摘要
The main aim of this paper is to study whether the Gromov hyperbolicity is preserved under some transformations on Riemann surfaces (with their Poincare 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.
The main aim of this paper is to study whether the Gromov hyperbolicity is preserved under some transformations on Riemann surfaces (with their Poincare 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.