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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

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Higher order Dehn functions for horospheres in products of Hadamard spaces

Gabriele Link
  • Corresponding author
  • Institut für Algebra und Geometrie, Karlsruher Institut für Technologie (KIT), Englerstr. 2, Gebäude 20.30, 76131 Karlsruhe, Germany
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Published Online: 2018-01-07 | DOI: https://doi.org/10.1515/advgeom-2017-0042

Abstract

Let X be a product of r locally compact and geodesically complete Hadamard spaces. We prove that the horospheres in X centered at regular boundary points of X are Lipschitz-(r − 2)-connected. If X has finite Assouad–Nagata dimension, then using the filling construction by R. Young in [10] this gives sharp bounds on higher order Dehn functions for such horospheres. Moreover, if Γ ⊂ Is(X) is a lattice acting cocompactly on X minus a union of disjoint horoballs, then we get a sharp bound on higher order Dehn functions for Γ. We deduce that apart from the Hilbert modular groups already considered by R. Young, every irreducible ℚ-rank one lattice acting on a product of r Riemannian symmetric spaces of the noncompact type is undistorted up to dimension r−1 and has k-th order Dehn function asymptotic to V(k+1)/k for all kr − 2.

Keywords: Hadamard space; horosphere; Dehn function

MSC 2010: 20F69

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About the article


Received: 2016-08-02

Published Online: 2018-01-07


Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2017-0042.

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