Interior curvature estimates for graphical curvature quotient equations

Abstract

We prove interior curvature estimates for admissible graphical solutions of curvature quotient equations in the range $3\leq k<n$ on the full G{\aa}rding cone $\Gamma_k$. No convexity, semiconvexity, or $\Gamma_{k+1}$-admissibility assumption is required. The proof combines a new quantitative compression inequality, a two-surface comparison and doubling argument, and a Pogorelov estimate.