A Morse lemma for quasigeodesics in symmetric spaces and euclidean buildings

Kapovich, Michael; Leeb, Bernhard; Porti, Joan

doi:10.2140/gt.2018.22.3827

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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

DOI: 10.2140/gt.2018.22.3827

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

Volume 22, issue 7 (2018)