Rigidity of polyhedral surfaces, I

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)241-302
Number of pages62
JournalJournal of Differential Geometry
Volume96
Issue number2
DOIs
StatePublished - Feb 2014

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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