Random ideal triangulations and the Weil-Petersson distance between finite degree covers of punctured Riemann surfaces

Details Random ideal triangulations and the Weil-Petersson distance between finite degree covers of punctured Riemann surfaces Random ideal triangulations and the Weil-Petersson distance between finite degree covers of punctured Riemann surfaces

2008-06-13

arxiv.org/abs/0806.2304v1

Mathematics

Geometric Topology

86 pages, 4 figures, one three-page flow chart

Scientific paper

We prove that any two finite-area non-compact hyperbolic Riemann surfaces S and T have finite covers that are arbitrarily close in the normalized Weil-Petersson metric, where we normalize by dividing the square of the metric by the area of the surface. In the case where T is the modular surface this reduces to showing that S has a finite cover with a proper ideal triangulation where most of the shear coordinates are small; we will construct such a cover out of a random collection of immersed ideal triangles in S.

Affiliated with

Also associated with

No associations

Rating

Random ideal triangulations and the Weil-Petersson distance between finite degree covers of punctured Riemann surfaces 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 Random ideal triangulations and the Weil-Petersson distance between finite degree covers of punctured Riemann surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random ideal triangulations and the Weil-Petersson distance between finite degree covers of punctured Riemann surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-123855