A combinatorial Yamabe flow in three dimensions

Research output: Contribution to journalArticle

29 Scopus citations

Abstract

A combinatorial version of Yamabe flow is presented based on Euclidean triangulations coming from sphere packings. The evolution of curvature is then derived and shown to satisfy a heat equation. The Laplacian in the heat equation is shown to be a geometric analogue of the Laplacian of Riemannian geometry, although the maximum principle need not hold. It is then shown that if the flow is nonsingular, the flow converges to a constant curvature metric.

Original languageEnglish (US)
Pages (from-to)791-808
Number of pages18
JournalTopology
Volume44
Issue number4
DOIs
StatePublished - Jul 1 2005

Keywords

  • Curvature flow
  • Discrete Riemannian geometry
  • Laplacian
  • Sphere packing
  • Yamabe flow

ASJC Scopus subject areas

  • Geometry and Topology

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