Regge's Einstein-Hilbert functional on the double tetrahedron

Daniel Champion, David A Glickenstein, Andrea Young

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

The double tetrahedron is the triangulation of the three-sphere gotten by gluing together two congruent tetrahedra along their boundaries. As a piecewise flat manifold, its geometry is determined by its six edge lengths, giving a notion of a metric on the double tetrahedron. We study notions of Einstein metrics, constant scalar curvature metrics, and the Yamabe problem on the double tetrahedron, with some reference to the possibilities on a general piecewise flat manifold. The main tool is analysis of Regges Einstein-Hilbert functional, a piecewise flat analogue of the Einstein-Hilbert (or total scalar curvature) functional on Riemannian manifolds. We study the Einstein-Hilbert-Regge functional on the space of metrics and on discrete conformal classes of metrics.

Original languageEnglish (US)
Pages (from-to)108-124
Number of pages17
JournalDifferential Geometry and its Application
Volume29
Issue number1
DOIs
Publication statusPublished - Feb 2011

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Keywords

  • Constant scalar curvature
  • Einstein
  • Einstein-Hilbert
  • Piecewise flat
  • Regge
  • Yamabe

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Analysis
  • Geometry and Topology

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