TY - JOUR
T1 - A Note on Discrete Einstein Metrics
AU - Ge , Huabin
AU - Mei , Jinlong
AU - Zhou , Da
JO - Journal of Mathematical Study
VL - 2
SP - 160
EP - 168
PY - 2019
DA - 2019/05
SN - 52
DO - http://doi.org/10.4208/jms.v52n2.19.03
UR - https://global-sci.org/intro/article_detail/jms/13156.html
KW - Discrete Einstein metric, Discrete Ricci flow.
AB - <p style="text-align: justify;">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 definition
of discrete Einstein metric than the former version. Finally, we introduce a discrete
Ricci flow for three dimensional triangulated manifolds, which is closely related to the
existence of discrete Einstein metrics.</p>