This result was presented by Fernando Alcalde at the conference Foliations 2014, that took place in Madrid, Spain, in September 2014.Corrigendum in "Discrete and continuous dynamical systems vol. 37 n° 8 (2017), 4585-4586 p. DOI: 10.3934/dcds.2017196International audienceWe consider a minimal compact lamination by hyperbolic surfaces. We prove that if it admits a leaf whose holonomy covering is not topologically trivial, then the horocycle flow on its unitary tangent bundle is minimal
Abstract. We study the growth and divergence of quotients of Kleinian groups G (i.e. discrete, torsionless groups of isometries of a Cartan-Hadamard manifold with pinched negative curvature). Namely, we give general criteria ensuring the divergence of a quotient groupḠ of G and the 'critical gap property' δḠ < δ G . As a corollary, we prove that every geometrically finite Kleinian group satisfying the parabolic gap condition (i.e. δ P < δ G for every parabolic subgroup P of G) is growth tight. These quotient groups naturally act on non-simply connected quotients of a Cartan-Hadamard manifold, so the classical arguments of Patterson-Sullivan theory are not available here; this forces us to adopt a more elementary approach, yielding as by-product a new elementary proof of the classical results of divergence for geometrically finite groups in the simply connected case. We construct some examples of quotients of Kleinian groups and discuss the optimality of our results.
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