Vol. 287, No. 1, 2017

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ISSN: 0030-8730
Three-dimensional discrete curvature flows and discrete Einstein metrics

Huabin Ge, Xu Xu and Shijin Zhang

Vol. 287 (2017), No. 1, 49–70
Abstract

A discrete version of the Einstein–Hilbert functional was introduced by Regge. In this paper, we define the discrete Einstein metrics as critical points of Regge’s Einstein–Hilbert functional with normalization on triangulated 3-manifolds. We also introduce some discrete curvature flows, which are closely related to the existence of discrete Einstein metrics.

Keywords
discrete Einstein–Hilbert functional, discrete Ricci curvature, discrete Ricci flow, discrete Einstein metric
Mathematical Subject Classification 2010
Primary: 53C44
Milestones
Received: 11 August 2015
Revised: 17 June 2016
Accepted: 22 September 2016
Published: 6 February 2017
Authors
Huabin Ge
Department of Mathematics
Beijing Jiaotong University
Beijing, 100044
China
Xu Xu
School of Mathematics and Statistics
Wuhan University
Wuhan, 430072
China
Shijin Zhang
School of Mathematics and Systems Science
Beihang University
Beijing, 100191
China