Quasi-geodesic segments and Gromov hyperbolic spaces

• DOI: 10.1007/bf00181569
• Publication Date: 2004-09-24T19:25:45Z
• Authors: Mario Bonk
• Keywords: Hyperbolicity; Science; Geometry; Quasi-geodesics; 0101 mathematics; 53C23; Stability; 01 natural sciences; Mathematics

It is known that for a geodesic metric space hyperbolicity in the sense of Gromov implies geodesic stability. In this paper it is shown that the converse is also true. So Gromov hyperbolicity and geodesic stability are equivalent for geodesic metric spaces. Mathematics Subject Classification (1991): 53C23.