A combinatorial Yamabe flow in three dimensions

Research output: Contribution to journalArticle

28 Citations (Scopus)

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 2005

Fingerprint

Three-dimension
Heat Equation
Curvature
Sphere packing
Riemannian geometry
Maximum Principle
Triangulation
Euclidean
Analogue
Converge
Metric

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

A combinatorial Yamabe flow in three dimensions. / Glickenstein, David A.

In: Topology, Vol. 44, No. 4, 07.2005, p. 791-808.

Research output: Contribution to journalArticle

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