Journal of Differential Geometry

Rigidity of polyhedral surfaces, I

Feng Luo

Full-text: Open access

Abstract

We study the rigidity of polyhedral surfaces and the moduli space of polyhedral surfaces using variational principles. Curvature-like quantities for polyhedral surfaces are introduced and are shown to determine the polyhedral metric up to isometry. The action functionals in the variational approaches are derived from the cosine law. They can be considered as 2-dimensional counterparts of the Schlaefli formula.

Article information

Source
J. Differential Geom., Volume 96, Number 2 (2014), 241-302.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1393424919

Digital Object Identifier
doi:10.4310/jdg/1393424919

Mathematical Reviews number (MathSciNet)
MR3178441

Zentralblatt MATH identifier
06287981

Citation

Luo, Feng. Rigidity of polyhedral surfaces, I. J. Differential Geom. 96 (2014), no. 2, 241--302. doi:10.4310/jdg/1393424919. https://projecteuclid.org/euclid.jdg/1393424919


Export citation