A Morse Lemma for quasigeodesics in symmetric spaces and euclidean buildings

Abstract

We prove a Morse Lemma for coarsely regular quasigeodesics in nonpositively curved symmetric spaces and euclidean buildings X. The main application is a simpler coarse geometric characterization of Morse subgroups of the isometry groups Isom(X) as undistorted subgroups which are coarsely uniformly regular. We show furthermore that they must be word hyperbolic. We introduced this class of discrete subgroups in our earlier paper, in the context of symmetric spaces, where various equivalent geometric and dynamical characterizations of word hyperbolic Morse subgroups were established, including the Anosov subgroup property.

Remark 1.11 regarding [GGKW] added

References in corpus (4)

• A Morse Lemma for quasigeodesics in symmetric spaces and euclidean buildings
• Anosov representations and proper actions
• Morse actions of discrete groups on symmetric space
• Finsler bordifications of symmetric and certain locally symmetric spaces

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• Morse actions of discrete groups on symmetric spaces: Local-to-global principle
• Representations and geometric structures
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• Compactification of certain Clifford-Klein forms of reductive homogeneous spaces
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• Nearly geodesic immersions and domains of discontinuity
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• Complete affine manifolds with Anosov holonomy groups