On the curvature of piecewise flat spaces

Jeff Cheeger, Werner Müller, Robert Schrader

Research output: Contribution to journalArticlepeer-review


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
Issue number3
StatePublished - Sep 1984

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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