We prove compactness of solutions of a fully nonlinear Yamabe problem satisfying a lower Ricci curvature bound, when the manifold is not conformally diffeomorphic to the standard sphere. This allows us to prove the existence of solutions when the associated cone Γ; satisfies μΓ;+≤1, which includes the σk-Yamabe problem for k not smaller than half of the dimension of the manifold.
All Science Journal Classification (ASJC) codes
- Compactness and existence of solutions
- Fully nonlinear Yamabe problem