A combinatorial Yamabe flow in three dimensions
Metric Geometry
2007-05-23 v1 Geometric Topology
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.
Cite
@article{arxiv.math/0506182,
title = {A combinatorial Yamabe flow in three dimensions},
author = {David Glickenstein},
journal= {arXiv preprint arXiv:math/0506182},
year = {2007}
}
Comments
20 pages, 5 figures. The paper arxiv:math.MG/0211195 was absorbed into its new version and this paper