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.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Geometry and Topology