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Rigidity of polyhedral surfaces. I. (English) Zbl 1386.52023

Summary: 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.

MSC:

52C25 Rigidity and flexibility of structures (aspects of discrete geometry)
52B70 Polyhedral manifolds
53C24 Rigidity results
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