Mathematics – Geometric Topology
Scientific paper
2010-10-15
Mathematics
Geometric Topology
17 pages, 1 figure
Scientific paper
This paper investigates several global rigidity issues for polyhedral surfaces including inversive distance circle packings. Inversive distance circle packings are polyhedral surfaces introduced by P. Bowers and K. Stephenson as a generalization of Andreev-Thurston's circle packing. They conjectured that inversive distance circle packings are rigid. Using a recent work of R. Guo on variational principle associated to the inversive distance circle packing, we prove rigidity conjecture of Bowers-Stephenson in this paper. We also show that each polyhedral metric on a triangulated surface is determined by various discrete curvatures introduced in our previous work, verifying a conjecture in \cite{Lu1}. As a consequence, we show that the discrete Laplacian operator determines a Euclidean polyhedral metric up to scaling.
No associations
LandOfFree
Rigidity of Polyhedral Surfaces, III 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 Rigidity of Polyhedral Surfaces, III, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rigidity of Polyhedral Surfaces, III will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-181473