2017/01/02 by Thomas Weighill, Weighill, Thomas
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.1701.00500
By a geodesic subspace of a metric space X we mean a subset A of X such that any two points in A can be connected by a geodesic in A. It is easy to check that a geodesic metric space X is an ℝ-tree (that is, a 0-hyperbolic space in the sense of Gromov) if and only if the union of any two intersecting geodesic subspaces is again a geodesic subspace. In this paper, we prove an analogous characterization of general Gromov hyperbolic spaces, where we replace geodesic subspaces by quasigeodesic subspaces.