%0 Generic %1 Luo2010 %A Luo, Feng %D 2010 %K circle packing polyhedral surfaces %T Rigidity of Polyhedral Surfaces, III %U http://arxiv.org/abs/1010.3284 %X 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 Lu1. As a consequence, we show that the discrete Laplacian operator determines a Euclidean polyhedral metric up to scaling.

@misc{Luo2010, abstract = { 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. }, added-at = {2010-10-20T08:16:49.000+0200}, author = {Luo, Feng}, biburl = {https://www.bibsonomy.org/bibtex/2508a4c8b9cedb8827e03da6e320bcda4/uludag}, description = {Rigidity of Polyhedral Surfaces, III}, interhash = {0d6f558e4ae754d2dc9f2a6883124dd3}, intrahash = {508a4c8b9cedb8827e03da6e320bcda4}, keywords = {circle packing polyhedral surfaces}, note = {cite arxiv:1010.3284 Comment: 17 pages, 1 figure}, timestamp = {2010-10-20T08:16:49.000+0200}, title = {Rigidity of Polyhedral Surfaces, III}, url = {http://arxiv.org/abs/1010.3284}, year = 2010 }