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.

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.

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## Additional indexing

Item Type: | Journal Article, refereed, original work |
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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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