We prove uniform Ancona—Gouëzel—Lalley inequalities for an extension by a hyperbolic group G of Markov map which allows to deduce that the visual boundary and Martin are Hölder equivalent. As application, we identify set minimal δ-conformal measures regular cover convex-cocompact CAT(-1)-manifold with covering group, provided this is hyperbolic. In setting, uniformity minimal, densities in sens...

It is well-known that a Kleinian group is amenable if and only if it is elementary. We establish an analogous property for equivalence relations and foliations with Gromov hyperbolic leaves: they are amenable if and only if they are elementary in the sense that one can assign (in a measurable way) to any leaf a finite subset of its hyperbolic boundary (as in the group case, such subsets cannot ...

In this paper, we prove that every metric line in the Poincare ball model of hyperbolic geometry is exactly a classical line of itself. We also proved nonexistence of periodic lines in the Poincare ball model of hyperbolic geometry.

We construct an example of a torsion free freely indecomposable nitely presented non quasiconvex subgroup H of a word hyperbolic group G such that the limit set of H is not the limit set of a quasiconvex subgroup of G In particular this gives a counterexample to the conjecture of G Swarup that a nitely presented one ended subgroup of a word hyperbolic group is quasiconvex if and only if it has ...

We define an extended Bloch group and show it is isomorphic to H3(PSL(2,C);Z). Using the Rogers dilogarithm function this leads to an exact simplicial formula for the universal Cheeger-Simons class on this homology group. It also leads to an independent proof of the analytic relationship between volume and Chern-Simons invariant of hyperbolic manifolds conjectured in [14] and proved in [17], as...

The present paper focuses on numerical study for an inclined magneto-hydrodynamic effect on free convection flow of a tangent hyperbolic nanofluid embedded with Carbon nanotubes (CNTs) over a stretching surface taking velocity and thermal slip into account. Two types of nanoparticles are considered for the study; they are single and multi-walled nanotubes. The presentation of single-parameter g...

Abstract. Let GL(2,H) be the group of invertible 2 × 2 matrices over the division algebra H of quaternions. GL(2,H) acts on the hyperbolic 5-space as the group of orientation-preserving isometries. Using this action we give an algebraic characterization of the dynamical types of the orientation-preserving isometries of the hyperbolic 5-space. Along the way we also determine the conjugacy classe...