Quasi-isometric maps between direct products of hyperbolic spaces

Quasi-isometric maps between direct products of hyperbolic spaces

We give conditions under which a quasi-isometric map between direct products of hyperbolic spaces splits as a direct product up to bounded distance and permutation of factors. This is a variation on a result due to Kapovich, Kleiner and Leeb.

Orbit Spaces Arising from Isometric Actions on Hyperbolic Spaces

Let be a differentiable action of a Lie group on a differentiable manifold and consider the orbit space with the quotient topology.  Dimension of is called the cohomogeneity of the action of  on . If is a differentiable manifold  of  cohomogeneity one under the action of  a compact and connected Lie group, then the orbit space is homeomorphic to one of the spaces , , or . In this paper we suppo...

Harmonic Maps between 3 - Dimensional Hyperbolic Spaces

We prove that a quasiconformal map of the sphere S admits a harmonic quasi-isometric extension to the hyperbolic space H, thus confirming the well known Schoen Conjecture in dimension 3.

Groups Quasi-isometric to Complex Hyperbolic Space

We show that any finitely generated group quasi-isometric to complex hyperbolic space is a finite extension of a properly discontinuous, cocompact subgroup of the isometry group.

Products of hyperbolic metric spaces