Anosov subgroups: dynamical and geometric characterizations

Michael Kapovich, Bernhard Leeb, Joan Porti

Research output: Contribution to journalArticleResearchpeer-review

44 Citations (Scopus)


© 2017, Springer International Publishing AG. We study infinite covolume discrete subgroups of higher rank semisimple Lie groups, motivated by understanding basic properties of Anosov subgroups from various viewpoints (geometric, coarse geometric and dynamical). The class of Anosov subgroups constitutes a natural generalization of convex cocompact subgroups of rank one Lie groups to higher rank. Our main goal is to give several new equivalent characterizations for this important class of discrete subgroups. Our characterizations capture “rank one behavior” of Anosov subgroups and are direct generalizations of rank one equivalents to convex cocompactness. Along the way, we considerably simplify the original definition, avoiding the geodesic flow. We also show that the Anosov condition can be relaxed further by requiring only non-uniform unbounded expansion along the (quasi)geodesics in the group.
Original languageEnglish
Pages (from-to)808-898
JournalEuropean Journal of Mathematics
Issue number4
Publication statusPublished - 1 Dec 2017


  • Anosov subgroups
  • Discrete subgroups
  • Symmetric spaces


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