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We prove that finitely generated higher dimensional Kleinian groups with small critical exponent are always convex-cocompact. Along the way, we also prove some geometric properties for any complete pinched negatively curved manifold with critical exponent less than 1.
In arXiv:1802.02833 Guichard and Wienhard introduced the notion of $Theta$-positivity, a generalization of Lusztigs total positivity to real Lie groups that are not necessarily split. Based on this notion, we introduce in this paper $Theta$-positive
We prove a theorem that gives a sufficient condition for the full basic automorphism group of a complete Cartan foliation to admit a unique (finite-dimensional) Lie group structure in the category of Cartan foliations. Emphasize that the transverse C
Let $X$ be a proper geodesic Gromov hyperbolic metric space and let $G$ be a cocompact group of isometries of $X$ admitting a uniform lattice. Let $d$ be the Hausdorff dimension of the Gromov boundary $partial X$. We define the critical exponent $del
If $Gamma$ is a discrete subgroup of $PSL(3,Bbb{C})$, it is determined the equicontinuity region $Eq(Gamma)$ of the natural action of $Gamma$ on $Bbb{P}^2_Bbb{C}$. It is also proved that the action restricted to $Eq(Gamma)$ is discontinuous, and $Eq(
We introduce $Theta$-positivity, a new notion of positivity in real semisimple Lie groups. The notion of $Theta$-positivity generalizes at the same time Lusztigs total positivity in split real Lie groups as well as well known concepts of positivity i