Year: 2019
Author: Huabin Ge, Jinlong Mei, Da Zhou
Journal of Mathematical Study, Vol. 52 (2019), Iss. 2 : pp. 160–168
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v52n2.19.03
Journal of Mathematical Study, Vol. 52 (2019), Iss. 2 : pp. 160–168
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: Discrete Einstein metric Discrete Ricci flow.