Hyperbolicity, CAT(-1)-spaces and the Ptolemy Inequality

2006/05/16 by Thomas Foertsch, Foertsch, Thomas, Viktor Schroeder +1
Mathematics · #53C20 #FOS: Mathematics #Metric Geometry (math.MG) #math.MG #msc:53C20

paper · pdf · doi:10.48550/arxiv.math/0605418

This updated version includes some further observations concerning the Ptolemy inequality. Some proofs have been improved and several typos have been corrected

arxiv created 2006/07/13 · arxiv updated 2009/12/01

Abstract

Using a four points inequality for the boundary of CAT(-1)-spaces, we study the relation between Gromov hyperbolic spaces and CAT(-1)-spaces.

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• Non-positive curvature and the Ptolemy inequality
• The Boundary at Infinity of a rough CAT(0) space
• Sharp Adams-Moser-Trudinger type inequalities in the hyperbolic space
• Sublinearly Morse Boundary I: CAT(0) Spaces