A combinatorial Yamabe flow in three dimensions

Details A combinatorial Yamabe flow in three dimensions A combinatorial Yamabe flow in three dimensions

2005-06-10

arxiv.org/abs/math/0506182v1

Topology 44 (2005) 791-808

Mathematics

Metric Geometry

20 pages, 5 figures. The paper arxiv:math.MG/0211195 was absorbed into its new version and this paper

Scientific paper

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.

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