A characterization of Gromov hyperbolicity of surfaces with variable negative curvature

Abstract

In this paper we show that, in order to check Gromov hyperbolicity of any surface with curvature $K \le -k^2<0$, we just need to verify the Rips condition on a very small class of triangles, namely, those contained in simple closed geodesics. This result is, in fact, a new characterization of Gromov hyperbolicity for this kind of surfaces.