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.
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Submitted: February 1999, Revised version: November 1999.
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Leuzinger, E. Corank and asymptotic filling-invariants for symmetric spaces . GAFA, Geom. funct. anal. 10, 863–873 (2000). https://doi.org/10.1007/PL00001641
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DOI: https://doi.org/10.1007/PL00001641