Scalar curvature and the existence of geometric structures on 3-manifolds, I

Details Scalar curvature and the existence of geometric structures on 3-manifolds, I Scalar curvature and the existence of geometric structures on 3-manifolds, I

2002-02-04

arxiv.org/abs/math/0202029v1

Mathematics

Differential Geometry

44pp. To appear in Jour. Reine Angew. Math

Scientific paper

This paper analyses the convergence and degeneration of sequences of metrics
on a 3-manifold, and relations of such with Thurston's geometrization
conjecture. The sequences are minimizing sequences for a certain (optimal)
scalar-curvature type functional and their degeneration is related to the
sphere and torus decompositions of the 3-manifold under certain conditions.

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