A maximum principle for combinatorial Yamabe flow

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22 Scopus citations

Abstract

This article studies a discrete geometric structure on triangulated manifolds and an associated curvature flow (combinatorial Yamabe flow). The associated evolution of curvature appears to be like a heat equation on graphs, but it can be shown to not satisfy the maximum principle. The notion of a parabolic-like operator is introduced as an operator which satisfies the maximum principle, but may not be parabolic in the usual sense of operators on graphs. A maximum principle is derived for the curvature of combinatorial Yamabe flow under certain assumptions on the triangulation, and hence the heat operator is shown to be parabolic-like. The maximum principle then allows a characterization of the curvature as well was a proof of long term existence of the flow.

Original languageEnglish (US)
Pages (from-to)809-825
Number of pages17
JournalTopology
Volume44
Issue number4
DOIs
StatePublished - Jul 1 2005

Keywords

  • Curvature flow
  • Discrete Riemannian geometry
  • Laplacians on graphs
  • Maximum principle
  • Sphere packing
  • Yamabe flow

ASJC Scopus subject areas

  • Geometry and Topology

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