Circle packings on surfaces with projective structures

Details Circle packings on surfaces with projective structures Circle packings on surfaces with projective structures

2001-11-20

arxiv.org/abs/math/0111214v2

J. Differential Geom., 63 (2003), 349-397

Mathematics

Geometric Topology

44 pages, 12 embedded figures; v2:very minor modification

Scientific paper

The Andreev-Thurston theorem states that for any triangulation of a closed orientable surface \Sigma_g of genus g which is covered by a simple graph in the universal cover, there exists a unique metric of curvature 1, 0 or -1 on the surface depending on whether g=0, 1 or \ge 2 such that the surface with this metric admits a circle packing with combinatorics given by the triangulation. Furthermore, the circle packing is essentially rigid, that is, unique up to conformal automorphisms of the surface isotopic to the identity. In this paper, we consider projective structures on the surface \Sigma_g where circle packings are also defined. We show that the space of projective structures on a surface of genus g \ge 2 which admits a circle packing by one circle is homeomorphic to R^{6g-6} and furthermore that the circle packing is rigid on such surfaces.

Affiliated with

Also associated with

No associations

Rating

Circle packings on surfaces with projective structures 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 Circle packings on surfaces with projective structures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Circle packings on surfaces with projective structures will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-275390