A priori estimates for the Yamabe problem in the non-locally conformally flat case

Marques, Fernando Coda

J. Differential Geom., Tome 69 (2005) no. 3, p. 315-346 / Harvested from Project Euclid

Résumé

Given a compact Riemannian manifold (Mⁿ, g), with positive Yamabe quotient, not conformally diffeomorphic to the standard sphere, we prove a priori estimates for solutions to the Yamabe problem. We restrict ourselves to the dimensions where the Positive Mass Theorem is known to be true, that is, when n ≤ 7. We also show that, when n ≥ 6, the Weyl tensor has to vanish at a point where solutions to the Yamabe equation blow up.

Publié le : 2005-10-14
Classification:

@article{1143651772,
     author = {Marques, Fernando Coda},
     title = {A priori estimates for the Yamabe problem in the non-locally conformally flat case},
     journal = {J. Differential Geom.},
     volume = {69},
     number = {3},
     year = {2005},
     pages = { 315-346},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1143651772}
}

Marques, Fernando Coda. A priori estimates for the Yamabe problem in the non-locally conformally flat case. J. Differential Geom., Tome 69 (2005) no. 3, pp.  315-346. http://gdmltest.u-ga.fr/item/1143651772/