The Thurston metric on hyperbolic domains and boundaries of convex hulls

Details The Thurston metric on hyperbolic domains and boundaries of convex hulls The Thurston metric on hyperbolic domains and boundaries of convex hulls

2010-02-09

arxiv.org/abs/1002.1929v2

Mathematics

Geometric Topology

Scientific paper

We show that the nearest point retraction is a uniform quasi-isometry from the Thurston metric on a hyperbolic domain in the Riemann sphere to the boundary of the convex hull of its complement. As a corollary, one obtains explicit bounds on the quasi-isometry constant of the nearest point retraction with respect to the Poincare metric when the domain is uniformly perfect. We also establish Marden and Markovic's conjecture that a hyperbolic domain is uniformly perfect if and only if the nearest point retraction is Lipschitz with respect to the Poincare metric.

Affiliated with

Also associated with

No associations

Rating

The Thurston metric on hyperbolic domains and boundaries of convex hulls does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Thurston metric on hyperbolic domains and boundaries of convex hulls, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Thurston metric on hyperbolic domains and boundaries of convex hulls will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-125204