%0 Journal Article
%T A combinatorial Yamabe flow in three dimensions
%A David Glickenstein
%J Mathematics
%D 2005
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0506182v1