The convex core of quasifuchsian manifolds with particles

Details The convex core of quasifuchsian manifolds with particles The convex core of quasifuchsian manifolds with particles

2009-09-23

arxiv.org/abs/0909.4182v1

Mathematics

Geometric Topology

38 pages, 1 figure

Scientific paper

We consider quasifuchsian manifolds with "particles", i.e., cone singularities of fixed angle less than $\pi$ going from one connected component of the boundary at infinity to the other. Each connected component of the boundary at infinity is then endowed with a conformal structure marked by the endpoints of the particles. We prove that this defines a homeomorphism from the space of quasifuchsian metrics with $n$ particles (of fixed angle) and the product of two copies of the Teichm\"uller space of a surface with $n$ marked points. This is analoguous to the Bers theorem in the non-singular case. Quasifuchsian manifolds with particles also have a convex core. Its boundary has a hyperbolic induced metric, with cone singularities at the intersection with the particles, and is pleated along a measured geodesic lamination. We prove that any two hyperbolic metrics with cone singularities (of prescribed angle) can be obtained, and also that any two measured bending laminations, satisfying some obviously necessary conditions, can be obtained, as in [BO] in the non-singular case.

Affiliated with

Also associated with

No associations

Rating

The convex core of quasifuchsian manifolds with particles 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 convex core of quasifuchsian manifolds with particles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The convex core of quasifuchsian manifolds with particles will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-181795