A Note on Discrete Einstein Metrics (Journal of Mathematical Study, 2019)
In this note, we prove that the space of all admissible piecewise linear metrics parameterized by the square of length on a triangulated manifold is a convex cone.We further study Regge’s Einstein-Hilbert action and give a more reasonable definitionof discrete Einstein metric than the former version. Finally, we introduce a discreteRicci flow for three dimensional triangulated manifolds, which is closely related to theexistence of discrete Einstein metrics.
Keywords: Discrete Einstein metric; Discrete Ricci flow.