The Boundary at Infinity of a rough CAT(0) space

2012/09/28 by Buckley, Stephen M., Falk, Kurt
#51M05 #51M10 (Primary) 51F99 (Secondary) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1209.6557

Abstract

We develop the boundary theory of rough CAT(0) spaces, a class of spaces that contains both Gromov hyperbolic and CAT(0) spaces. The resulting theory generalizes the common features of the Gromov boundary of a Gromov hyperbolic space and the ideal boundary of a complete CAT(0) space. It is not assumed that the spaces are geodesic or proper.

Related

• Rough CAT(0) spaces
• Sublinearly Morse Boundary I: CAT(0) Spaces
• Curtain Characterization of Sublinearly Morse Geodesics in CAT(0) Spaces
• Natural maps between CAT(0) boundaries
• On the capacity dimension of the boundary of CAT(0) spaces