Scalar curvature and the existence of geometric structures on 3-manifolds. I. (English summary) J. Reine Angew. Math. 553 (2002), 125–182. Summary: “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.” The genesis of the idea of using the solutions to the Yamabe problem to approach the Poincaré Conjecture was originated by Yamabe and then developed further by Schoen, in terms of the minimax method, who also solved the long standing Yamabe problem using the positive mass theorem of Schoen and Yau, along with earlier works by Trudinger and Aubin
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