A combinatorial Yamabe flow in three dimensions
Copyright policy )A combinatorial Yamabe flow in three dimensions
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.
20 pages, 5 figures. The paper arxiv:math.MG/0211195 was absorbed into its new version and this paper
- University of Arizona United States
Curvature flow, Discrete Riemannian geometry, discrete Riemannian geometry, Heat equation, Triangulating manifolds, curvature flow, Metric Geometry (math.MG), Geometric Topology (math.GT), Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Sphere packing, Mathematics - Geometric Topology, 52C26, Mathematics - Metric Geometry, sphere packing, Yamabe flow, FOS: Mathematics, Geometry and Topology, Laplacian, Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Curvature flow, Discrete Riemannian geometry, discrete Riemannian geometry, Heat equation, Triangulating manifolds, curvature flow, Metric Geometry (math.MG), Geometric Topology (math.GT), Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Sphere packing, Mathematics - Geometric Topology, 52C26, Mathematics - Metric Geometry, sphere packing, Yamabe flow, FOS: Mathematics, Geometry and Topology, Laplacian, Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
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