Journal of Differential Geometry

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

Fernando Coda Marques

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Abstract

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.

Article information

Source
J. Differential Geom., Volume 71, Number 2 (2005), 315-346.

Dates
First available in Project Euclid: 29 March 2006

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1143651772

Digital Object Identifier
doi:10.4310/jdg/1143651772

Mathematical Reviews number (MathSciNet)
MR2197144

Zentralblatt MATH identifier
1101.53019

Citation

Marques, Fernando Coda. A priori estimates for the Yamabe problem in the non-locally conformally flat case. J. Differential Geom. 71 (2005), no. 2, 315--346. doi:10.4310/jdg/1143651772. https://projecteuclid.org/euclid.jdg/1143651772


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