Geodesic
Deforming three-manifolds with positive scalar curvature
Fernando C. Marques1
1 Instituto de Matemática Pura e Aplicada (IMPA)<br/> Estrada Dona Castorina 110<br/> 22460-320 Rio de Janeiro<br/> Brazil
Annals of mathematics, Tome 176 (2012) no. 2, pp. 815-863.

Voir la notice de l'article provenant de la source Annals of Mathematics website

In this paper 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 $\mathbb{R}^3$.
DOI : 10.4007/annals.2012.176.2.3

Fernando C. Marques 1

1 Instituto de Matemática Pura e Aplicada (IMPA)<br/> Estrada Dona Castorina 110<br/> 22460-320 Rio de Janeiro<br/> Brazil 
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Fernando C. Marques. Deforming  three-manifolds with positive scalar curvature. Annals of mathematics, Tome 176 (2012) no. 2, pp. 815-863. doi : 10.4007/annals.2012.176.2.3. http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.176.2.3/

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