On the curvature of piecewise flat spaces

Jeff Cheeger; Werner Müller; Robert Schrader

doi:10.1007/BF01210729

On the curvature of piecewise flat spaces

Jeff Cheeger, Werner Müller, Robert Schrader

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider analogs of the Lipschitz-Killing curvatures of smooth Riemannian manifolds for piecewise flat spaces. In the special case of scalar curvature, the definition is due to T. Regge; considerations in this spirit date back to J. Steiner. We show that if a piecewise flat space approximates a smooth space in a suitable sense, then the corresponding curvatures are close in the sense of measures.

Original language	English (US)
Pages (from-to)	405-454
Number of pages	50
Journal	Communications In Mathematical Physics
Volume	92
Issue number	3
DOIs	https://doi.org/10.1007/BF01210729
State	Published - Sep 1984

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01210729

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title = "On the curvature of piecewise flat spaces",

abstract = "We consider analogs of the Lipschitz-Killing curvatures of smooth Riemannian manifolds for piecewise flat spaces. In the special case of scalar curvature, the definition is due to T. Regge; considerations in this spirit date back to J. Steiner. We show that if a piecewise flat space approximates a smooth space in a suitable sense, then the corresponding curvatures are close in the sense of measures.",

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On the curvature of piecewise flat spaces

Abstract

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