Rigidity of polyhedral surfaces I

Feng Luo Rutgers University

Differential Geometry Geometric Analysis and Geometric Topology mathscidoc:1705.10005

Distinguished Paper Award in 2017

J. Differential Geometry, 96, (2), 241-302, 2014
We study the rigidity of polyhedral surfaces and the moduli space of polyhedral surfaces using variational principles. Curvaturelike 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.
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  title={Rigidity of polyhedral surfaces I},
  author={Feng Luo},
  booktitle={J. Differential Geometry},
Feng Luo. Rigidity of polyhedral surfaces I. 2014. Vol. 96. In J. Differential Geometry. pp.241-302. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170531091115350195782.
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