  We define Discrete Quasi-Einstein metrics (DQE-metrics) as the critical
points of discrete total curvature functional on triangulated 3-manifolds. We
study DQE-metrics by introducing some combinatorial curvature flows. We prove
that these flows produce solutions which converge to discrete quasi-Einstein
metrics when the initial energy is small enough. The proof relies on a careful
analysis of discrete dual-Laplacians which we interpret as the Jacobian matrix
of the curvature map. As a consequence, combinatorial curvature flow provides
an algorithm to compute discrete sphere packing metrics with prescribed
curvatures.
