Main References:

1. S. Y. A. Chang, M. J. Gursky and P. Yang, An equation of Monge-Ampere type in conformal geometry, and four-manifolds of positive Ricci curvature.
   https://www.jstor.org/stable/pdf/3062131.pdf?casa_token=1P2pYhxqcSYAAAAA:CdjosjYO4t9lmjHDCC7OBzmgkY_PNKHeJBOomR7j2t0H0yWmQUTQFCnH8Sg6BeMP6NVdFUwrXgG4Bk338qMa7yHor2dQBVCCH8vrCv8MGiRD-5Hqm2U 
2. S. Y. A. Chang, M. J. Gursky and P. Yang, An a priori estimate for a fully nonlinear equation on four-manifolds
   https://link.springer.com/content/pdf/10.1007/BF02868472.pdf
3. Simon Brendle, Jeff A. Viaclovsky, A variational characterization for $\sigma_{n/2}$
   https://link.springer.com/content/pdf/10.1007%2Fs00526-003-0234-9.pdf