Three-dimensional discrete curvature flows and discrete Einstein metrics

Huabin Ge, Xu Xu and Shijin Zhang

Vol. 287 (2017), No. 1, 49–70

DOI: 10.2140/pjm.2017.287.49

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