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arXiv · 1007.0048

Regge's Einstein-Hilbert Functional on the Double Tetrahedron

Daniel Champion·David Glickenstein·Andrea Young
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Abstract

The double tetrahedron is the triangulation of the three-sphere gotten by gluing together two congruent tetrahedra along their boundaries. As a piecewise flat manifold, its geometry is determined by its six edge lengths, giving a notion of a metric on the double tetrahedron. We study notions of Einstein metrics, constant scalar curvature metrics, and the Yamabe problem on the double tetrahedron, with some reference to the possibilities on a general piecewise flat manifold. The main tool is analysis of Regge's Einstein-Hilbert functional, a piecewise flat analogue of the Einstein-Hilbert (or total scalar curvature) functional on Riemannian manifolds. We study the Einstein-Hilbert-Regge functional on the space of metrics and on discrete conformal classes of metrics.

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Daniel Champion, David Glickenstein, Andrea Young. 2010-06-30. Regge's Einstein-Hilbert Functional on the Double Tetrahedron. https://arxiv.org/abs/1007.0048

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