We establish interior estimates for convex solutions of the scalar curvature equation and the -Hessian equation. We also prove interior curvature estimates for isometrically immersed hypersurfaces with positive scalar curvature. These estimates are consequences of interior estimates for these equations obtained under a weakened condition.
"Interior regularity of convex solutions to prescribing scalar curvature equations." Duke Math. J. 168 (9) 1641 - 1663, 15 June 2019. https://doi.org/10.1215/00127094-2019-0001