A Morse lemma for quasigeodesics in symmetric spaces and euclidean buildings

By Michael Kapovich, B. Leeb, J. Porti. Geometry and Topology, 2014

118 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cd8eabb0f1726d05c1d36da5b4ba2e4a3e1625e6

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In Applied Mathematics

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Citations in the corpus

Geometric Group Theory (2018, background): “Nevertheless, some versions of the Morse Lemma remain true for non-hyperbolic CAT (0) spaces, see [Sul14] and [KLP14].”
Conformality for a robust class of non-conformal attractors (2019, background): “Such representations provide the appropriate generalization of the class of convex co-compact subgroups in the context of Lie groups of higher rank [27, 31, 32].”
Finsler bordifications of symmetric and certain locally symmetric spaces (2015, background): “URU. 82 4. Γ is τmod-RCA. 5. Γ is τmod-asymptotically embedded. 6. Γ is τmod-Anosov. 7. Γ is S-cocompact. Proof. The implications 1ñ2ñ3are immediate. The equivalence 3ô4 is one of the main results of [KLP3], see Corollary 1.6 of that paper. The equivalences 4ô5ô6 are established in [KLP2]. The impli”
Dynamics on flag manifolds: domains of proper discontinuity and cocompactness (2013, methodology): “We give a geometric treatment and present the material in a form suitable for the further development of our theory of discrete isometry groups acting on Riemannian symmetric spaces and euclidean buildings, such as in our papers [16; 20].”
Anosov subgroups: dynamical and geometric characterizations (2017, methodology): “In our related work, they lay the basis for the results on the Higher Rank Morse Lemma [KLP3], compactifications of locally symmetric spaces for Anosov subgroups [KL1], the local-to-global principle and the construction of Morse-Schottky subgroups [KLP2].”