Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Characterizing complete $ \operatorname{CAT}(\kappa )$-spaces, $ \kappa <0$, with geodesic boundary


Authors: Thomas Foertsch and Katrin Radke
Journal: Trans. Amer. Math. Soc. 363 (2011), 75-93
MSC (2010): Primary 53C23, 53C24
DOI: https://doi.org/10.1090/S0002-9947-2010-05144-X
Published electronically: August 27, 2010
MathSciNet review: 2719672
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We investigate the Bourdon and Hamenstädt boundaries of complete $ \operatorname{CAT}(\kappa )$-spaces, $ \kappa <0$, and characterize those with geodesic Hamenstädt boundary up to isometry.


References [Enhancements On Off] (What's this?)

  • [AB1] S.B. Alexander & R.L. Bishop, Warped products of Hadamard spaces, Manuscripta Math. 96 (1998), 487-505 MR 1639844 (99g:53070)
  • [AB2] S.B. Alexander & R.L. Bishop, Curvature bounds for warped products of metric spaces, Geom. Funct. Anal., vol. 14 (2004), 1143-1181 MR 2135163 (2007d:53061)
  • [BF1] M. Bonk & T. Foertsch, Asymptotic upper curvature bounds in coarse geometry, Math. Z. 253 (2006), 753-785 MR 2221098 (2007e:53042)
  • [BF2] M. Bonk & T. Foertsch, Asymptotic lower curvature bounds in coarse geometry, preprint 2007
  • [BO'N] R.L. Bishop & B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969) 1-49 MR 0251664 (40:4891)
  • [BS] M. Bonk & O. Schramm, Embeddings of Gromov hyperbolic spaces, Geom. Funct. Anal. 10, no. 2 (2000), 266-306 MR 1771428 (2001g:53077)
  • [B] M. Bourdon, Structure conforme au bord et flot géodésique d'un $ \operatorname{CAT}(-1)$-espace, Enseign. Math. (2) no. 41 (1995), 63-102. MR 1341941 (96f:58120)
  • [BuS] S. Buyalo & V. Schroeder, Elements of asymptotic geometry, EMS Monographs in Mathematics. European Mathematical Society (EMS), Zürich, 2007. xii+200 pp. MR 2327160 (2009a:53068)
  • [C] C.H. Chen, Warped products of metric spaces of curvature bounded from above, Trans. Amer. Math. Soc., vol. 351, no. 12 (1999), 4727-4740 MR 1466944 (2000c:53031)
  • [FLS] T. Foertsch & A. Lytchak & V. Schroeder, Nonpositive curvature and the Ptolemy inequality, Int. Math. Res. Not. 2007, No. 22 (2007). MR 2376212 (2009d:53049a)
  • [FS1] T. Foertsch & V. Schroeder, A product construction for hyperbolic metric spaces, Illinois Journal of Mathematics, vol. 49, no. 3 (2005), 793-810 MR 2210259 (2006m:53059)
  • [FS2] T. Foertsch & V. Schroeder, Hyperbolicity, $ \operatorname{CAT}(-1)$-spaces and the Ptolemy Inequality, to appear in Math. Ann.
  • [Gr] M. Gromov, Hyperbolic groups, Essays in group theory, Math. Sci. Res. Inst. Publ., 8, Springer, New York, 1987, 75-263 MR 919829 (89e:20070)
  • [H] U. Hamenstädt, A new description of the Bowen-Margulis measure, Ergodic Theory Dynam. Systems 9 (1989), no. 3, 455-464. MR 1016663 (91b:58191)
  • [LS] U. Lang & T. Schlichenmaier, Nagata dimension, quasisymmetric embeddings, and Lipschitz extensions, Int. Math. Res. Not., no. 58 (2005), 3625-3655 MR 2200122 (2006m:53061)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 53C23, 53C24

Retrieve articles in all journals with MSC (2010): 53C23, 53C24


Additional Information

Thomas Foertsch
Affiliation: Mathematisches Institut, Universität Bonn, 53115 Bonn, Germany
Email: foertsch@math.uni-bonn.de

Katrin Radke
Affiliation: Mathematisches Institut, Universität Bonn, 53115 Bonn, Germany

DOI: https://doi.org/10.1090/S0002-9947-2010-05144-X
Received by editor(s): June 15, 2008
Published electronically: August 27, 2010
Article copyright: © Copyright 2010 American Mathematical Society

American Mathematical Society