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Deforming three-manifolds with positive scalar curvature. (English) Zbl 1319.53028

Summary: We prove that the moduli space of metrics with positive scalar curvature of an orientable compact three-manifold is path-connected. The proof uses the Ricci flow with surgery, the conformal method, and the connected sum construction of Gromov and Lawson. The work of Perelman on Hamilton’s Ricci flow is fundamental. As one of the applications we prove the path-connectedness of the space of trace-free asymptotically flat solutions to the vacuum Einstein constraint equations on \(\mathbb{R}^3\).

MSC:

53C20 Global Riemannian geometry, including pinching
58D17 Manifolds of metrics (especially Riemannian)
58D27 Moduli problems for differential geometric structures
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