Gromov hyperbolicity of Riemann surfaces (Q884879)

In this paper, the authors study the Gromov hyperbolicity of surfaces which are hyperbolic in the classical sense, that is, surfaces equipped with metrics of constant curvature \(-1\). Of course, the surfaces considered are non compact; they can have infinite genus and an infinite number of boundary components. The Gromov hyperbolicity results involve a decomposition of the given surface into pieces which are funnels or Y-pieces (that is, hyperbolic pairs of pants withe some of the boundary geodesics allowed be punctures), and the hyperbolicity of a certain graph which the authors associate to the surface. The paper contains some useful formulae involving basic hyperbolic trigonometry. The results in this paper are complements to results published by the same authors in previous papers.