Scalar curvature, isoperimetric collapse and General Relativity in the Constant Mean Curvature gauge

Details Scalar curvature, isoperimetric collapse and General Relativity in the Constant Mean Curvature gauge Scalar curvature, isoperimetric collapse and General Relativity in the Constant Mean Curvature gauge

2010-02-17

arxiv.org/abs/1002.3302v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages

Scientific paper

We discuss a set of relations, set in the form of results, conjectures and problems, between the L^{2}-norm of the Ricci curvature of a 3-manifold, the scalar curvature and the volume radius. We illustrate the scope of these relations with potential applications to the Einstein Constant Mean Curvature flow (or GR seen as a geometric flow of constant mean curvature), but we believe the framework has it own geometric interest.

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