Rigidity of polyhedral surfaces, II
Geometric Topology
2014-11-11 v1 Differential Geometry
Abstract
We study the rigidity of polyhedral surfaces using variational principle. The action functionals are derived from the cosine laws. The main focus of this paper is on the cosine law for a non-triangular region bounded by three possibly disjoint geodesics. Several of these cosine laws were first discovered and used by Fenchel and Nielsen. By studying the derivative of the cosine laws, we discover a uniform approach on several variational principles on polyhedral surfaces with or without boundary. As a consequence, the work of Penner, Bobenko-Springborn and Thurston on rigidity of polyhedral surfaces and circle patterns are extended to a very general context.
Keywords
Cite
@article{arxiv.0711.0766,
title = {Rigidity of polyhedral surfaces, II},
author = {Ren Guo and Feng Luo},
journal= {arXiv preprint arXiv:0711.0766},
year = {2014}
}
Comments
37 pages, 23 figures