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A Morse lemma for quasigeodesics in symmetric spaces and euclidean buildings

Michael Kapovich, Bernhard Leeb and Joan Porti

Geometry & Topology 22 (2018) 3827–3923
Abstract

We prove a Morse lemma for regular quasigeodesics in nonpositively curved symmetric spaces and euclidean buildings. We apply it to give a new coarse geometric characterization of Anosov subgroups of the isometry groups of such spaces simply as undistorted subgroups which are uniformly regular.

Keywords
symmetric spaces, buildings, quasigeodesics
Mathematical Subject Classification 2010
Primary: 53C35
Secondary: 20F65, 51E24
References
Publication
Received: 18 February 2016
Accepted: 11 May 2018
Published: 6 December 2018
Proposed: Bruce Kleiner
Seconded: Tobias H Colding, Dmitri Burago
Authors
Michael Kapovich
Department of Mathematics
University of California, Davis
Davis, CA
United States
Bernhard Leeb
Mathematisches Institut
Universität München
München
Germany
Joan Porti
Departament de Matemàtiques
Universitat Autònoma de Barcelona
Bellaterra
Spain