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On the curvature of piecewise flat spaces

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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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Authors and Affiliations

  1. Department of Mathematics, SUNY at Stony Brook, 11794, Stony Brook, NY, USA

    Jeff Cheeger

  2. Zentralinstitut für Mathematik, Akademie der Wissenschaften der DDR, Mohrenstrasse 39, DDR-1199, Berlin, German Democratic Republic

    Werner Müller

  3. Institute for Theoretical Physics, SUNY at Stony Brook, 11794, Stony Brook, NY, USA

    Robert Schrader

Authors
  1. Jeff Cheeger
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  2. Werner Müller
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  3. Robert Schrader
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Additional information

Communicated by A. Jaffe

Supported in part by NSF MCS-810-2758-A-02

Supported in part by Deutsche Forschungsgemeinschaft and NSF PHY-81-09110-A-01

On leave of absence from Freie Universität Berlin

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Cheeger, J., Müller, W. & Schrader, R. On the curvature of piecewise flat spaces. Commun.Math. Phys. 92, 405–454 (1984). https://doi.org/10.1007/BF01210729

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  • DOI: https://doi.org/10.1007/BF01210729

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