Interior Curvature Estimates for the Graphical Scalar Curvature Equation in All Dimensions

We resolve the long-standing problem of establishing interior $C^2$ estimates for admissible solutions of the graphical scalar curvature equation in every dimension $n\ge 3$. More precisely, we prove interior curvature estimates for admissible solutions to the constant graphical scalar curvature equation. The proof combines Jacobi inequalities with a two-surface maximum principle and a two-surface Pogorelov estimate.