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

2002/02/04 by Michael T. Anderson, Anderson, Michael T.
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.DG #math.GT

paper · pdf · doi:10.48550/arxiv.math/0202029

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

arxiv created 2002/02/04 · arxiv updated 2009/11/30

Abstract

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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