Displaying similar documents to “Addendum to: Crofton formulae and geodesic distance in hyperbolic spaces.”

Cannon-Thurston Maps, i-bounded Geometry and a Theorem of McMullen

Mahan Mj (2009-2010)

Séminaire de théorie spectrale et géométrie

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The notion of generalises simultaneously and the geometry of punctured torus Kleinian groups. We show that the limit set of a surface Kleinian group of i-bounded geometry is locally connected by constructing a natural Cannon-Thurston map.

Quasi-Isometries Need Not Induce Homeomorphisms of Contracting Boundaries with the Gromov Product Topology

Christopher H. Cashen (2016)

Analysis and Geometry in Metric Spaces

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We consider a ‘contracting boundary’ of a proper geodesic metric space consisting of equivalence classes of geodesic rays that behave like geodesics in a hyperbolic space.We topologize this set via the Gromov product, in analogy to the topology of the boundary of a hyperbolic space. We show that when the space is not hyperbolic, quasi-isometries do not necessarily give homeomorphisms of this boundary. Continuity can fail even when the spaces are required to be CAT(0). We show this by...