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Geometric & Functional Analysis GAFA

, Volume 10, Issue 4, pp 863–873 | Cite as

Corank and asymptotic filling-invariants for symmetric spaces

  • E. Leuzinger

Abstract.

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.

Keywords

Symmetric Space Sectional Curvature Geodesic Line Riemannian Symmetric Space Noncompact Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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