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Affine functions on CAT (κ)-spaces

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Abstract

We describe affine functions on spaces with an upper curvature bound.

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References

  1. Adams S., Ballmann W. (1998) Amenable isometry groups of Hadamard spaces. Math. Ann. 312, 183–195

    Article  MATH  MathSciNet  Google Scholar 

  2. Alexander S., Bishop R. (2005) A cone splitting theorem for Alexandrov spaces. Pac. J. Math. 218, 1–16

    MATH  MathSciNet  Google Scholar 

  3. Bernig A., Foertsch Th., Schroeder V. (2003) Nonstandard metric products. Beitr. Algebra Geom. 44, 499–510

    MATH  MathSciNet  Google Scholar 

  4. Bridson M., Haefliger A. (1999) Metric Spaces of Non-positive Curvature. Springer, Berlin Heidelberg

    MATH  Google Scholar 

  5. Innami N. (1982) Splitting theorems of Riemannian manifolds. Compositio Math. 47, 237–247

    MATH  MathSciNet  Google Scholar 

  6. Kleiner B. (1999) The local structure of length spaces with curvature bounded above. Math. Z. 231(3): 409–456

    Article  MATH  MathSciNet  Google Scholar 

  7. Lytchak A. (2004) Differentiation in metric spaces. Algebra i Analiz. 16(6): 128–161

    MathSciNet  Google Scholar 

  8. Lytchak, A., Nagano, K. Geodesically complete spaces with an upper curvature bound. (in preparation)

  9. Mashiko Y. (1999) Affine functions on Alexandrov surfaces. Osaka J. Math. 36, 853–859

    MATH  MathSciNet  Google Scholar 

  10. Mashiko Y. (2002) A splitting theorem for Alexandrov spaces. Pac. J. Math. 204, 445–458

    Article  MATH  MathSciNet  Google Scholar 

  11. Plaut, C. Metric spaces of curvature \(\geq k\). Handbook of Geometric Topology, pp 819–898. North-Holland, Amsterdam (2002)

  12. Toruńczyk H. (1978) Concerning locally homotopy negligible sets and characterization of l 2-manifolds. Fund. Math. 101, 93–110

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Mathematisches Institut, Universität Bonn, Beringstrasse 1, 53115, Bonn, Germany

    Alexander Lytchak

  2. Institut für Mathematik, Universität Zürich, Winterthurer Strasse 190, 8057, Zürich, Switzerland

    Viktor Schroeder

Authors
  1. Alexander Lytchak
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  2. Viktor Schroeder
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Correspondence to Alexander Lytchak.

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Lytchak, A., Schroeder, V. Affine functions on CAT (κ)-spaces. Math. Z. 255, 231–244 (2007). https://doi.org/10.1007/s00209-006-0020-4

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  • DOI: https://doi.org/10.1007/s00209-006-0020-4

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