Geometric & Functional Analysis GAFA

, Volume 10, Issue 4, pp 863–873

Corank and asymptotic filling-invariants for symmetric spaces

  • E. Leuzinger

DOI: 10.1007/PL00001641

Cite this article as:
Leuzinger, E. GAFA, Geom. funct. anal. (2000) 10: 863. doi:10.1007/PL00001641


Let X be a Riemannian symmetric space of noncompact type. We prove that there exists an embedded submanifold \( Y \subset X \) which is quasi-isometric to a manifold with strictly negative sectional curvature, which intersects a given flat F in a geodesic line and which satisfies dim(Y) — 1 = dim(X) — rank(X). This yields an estimate of the hyperbolic corank of X. As another application we show that certain asymptotic filling invariants of X are exponential.

Copyright information

© Birkhäuser Verlag, Basel 2000

Authors and Affiliations

  • E. Leuzinger
    • 1
  1. 1.Math. Institut II, Universität Karlsruhe, D-76128 Karlsruhe, Germany, e-mail: Enrico.Leuzinger@math.uni-karlsruhe.deDE

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