On the curvature of piecewise flat spaces

Jeff Cheeger, Werner Müller, Robert Schrader

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)405-454
Number of pages50
JournalCommunications in Mathematical Physics
Volume92
Issue number3
DOIs
StatePublished - Sep 1984

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Curvature
curvature
Smooth Manifold
Scalar Curvature
Date
Lipschitz
Riemannian Manifold
analogs
scalars
Analogue

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

On the curvature of piecewise flat spaces. / Cheeger, Jeff; Müller, Werner; Schrader, Robert.

In: Communications in Mathematical Physics, Vol. 92, No. 3, 09.1984, p. 405-454.

Research output: Contribution to journalArticle

Cheeger, Jeff ; Müller, Werner ; Schrader, Robert. / On the curvature of piecewise flat spaces. In: Communications in Mathematical Physics. 1984 ; Vol. 92, No. 3. pp. 405-454.
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