Skip to main content
Log in

Rigidity of invariant convex sets in symmetric spaces

  • Published:
Inventiones mathematicae Aims and scope

Abstract

The main result implies that a proper convex subset of an irreducible higher rank symmetric space cannot have Zariski dense stabilizer.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Anderson, M.T.: The Dirichlet problem at infinity for manifolds of negative curvature. J. Differ. Geom. 18, 701–721 (1984)

    Google Scholar 

  2. Ballmann, W.: Lectures on spaces of nonpositive curvature. DMV Seminar, vol. 25, with an appendix by Misha Brin. Basel: Birkhäuser 1995

  3. Balser, A., Lytchak, A.: Centers of convex subsets of buildings. To appear in Ann. Glob. Anal. Geom., ArXiv preprint math.MG/0410440

  4. Benoist, Y.: Propriétés asymptotiques des groupes linéaires. Geom. Funct. Anal. 7, 1–47 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  5. Borel, A., Tits, J.: Éléments unipotents et sous-groupes paraboliques de groupes réductifs. I. Invent. Math. 12, 95–104 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bridson, M.R., Haefliger, A.: Metric spaces of non-positive curvature. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 319. Berlin: Springer 1999

  7. Innami, N.: Splitting theorems of riemannian manifolds. Compos. Math. 47, 237–247 (1982)

    MATH  MathSciNet  Google Scholar 

  8. Kleiner, B., Leeb, B.: Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings. Publ. Math., Inst. Hautes Étud. Sci. 86, 115–197 (1997)

    MATH  MathSciNet  Google Scholar 

  9. Mostow, G.D.: Some new decomposition theorems for semi-simple groups. Mem. Am. Math. Soc. 14, 31–54 (1955)

    MATH  MathSciNet  Google Scholar 

  10. Quint, J.-F.: Groupes convexes cocompacts en rang supérieur. To appear in Geom. Dedicata, preprint 2004

  11. Ronan, M.: Lectures on buildings. Perspectives in Mathematics, vol. 7. Boston, MA: Academic Press Inc. 1989

  12. Tits, J.: Buildings of spherical type and finite BN-pairs. Lect. Notes Math., vol. 386. Berlin: Springer 1974

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kleiner, B., Leeb, B. Rigidity of invariant convex sets in symmetric spaces. Invent. math. 163, 657–676 (2006). https://doi.org/10.1007/s00222-005-0471-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00222-005-0471-y

Keywords

Navigation