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Quasiflats in Hadamard spaces


Lang, U; Schroeder, V (1997). Quasiflats in Hadamard spaces. Annales Scientifiques de l'Ecole Normale Superieure, 30(3):339-352.

Abstract

Let X be a simply connected, complete geodesic metric space which is nonpositively curved in the sense of Alexandrov. We assume that X contains a k-flat F of maximal dimension and consider quasiisometric embeddings f : ℝk → X whose distance function from F satisfies a certain asymptotic growth condition. We prove that if X is locally compact and cocompact, then the Hausdorff distance between f(ℝk) and F is uniformly bounded. This generalizes a well-known lemma of Mostow on quasiflats in symmetric spaces of noncompact type.

Abstract

Let X be a simply connected, complete geodesic metric space which is nonpositively curved in the sense of Alexandrov. We assume that X contains a k-flat F of maximal dimension and consider quasiisometric embeddings f : ℝk → X whose distance function from F satisfies a certain asymptotic growth condition. We prove that if X is locally compact and cocompact, then the Hausdorff distance between f(ℝk) and F is uniformly bounded. This generalizes a well-known lemma of Mostow on quasiflats in symmetric spaces of noncompact type.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1997
Deposited On:29 Nov 2010 16:28
Last Modified:05 Apr 2016 13:26
Publisher:Elsevier
ISSN:0012-9593
Free access at:Related URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1016/S0012-9593(97)89923-5
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1443490
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0876.53050
http://www.numdam.org/item?id=ASENS_1997_4_30_3_339_0

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