  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.
