δ-Hyperbolic Spaces and Area

  • Martin R. Bridson
  • André Haefliger
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 319)


In Part II we explored the geometry of spaces whose curvature is bounded above in a strict, local, sense by means of the CAT(к) inequality. In the non-positively curved case, the Cartan-Hadamard Theorem (II.4.1) allowed us to use this local information to make deductions about the global geometry of the universal coverings of the spaces under consideration. In this way we were able to generalize classical results concerning the global geometry of complete, simply connected manifolds of negative and non-positive curvature.


Hyperbolic Space Cayley Graph Isoperimetric Inequality Geodesic Segment Geodesic Triangle 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Martin R. Bridson
    • 1
  • André Haefliger
    • 2
  1. 1.Mathematical InstituteUniversity of OxfodOxfordGreat Britain
  2. 2.Section de MathématiquesUniversité de GenèveGenève 24Switzerland

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