Interior Hessian estimates for k-convex solutions of Hessian quotient equations with 2k>n

Abstract

We establish interior Hessian estimates for $k$ convex solutions of $\frac{\sigma_k(D^2u)}{\sigma_l(D^2u)}=1$, where $1 \leq l<k<n$, $k-l \in \{1,2\}$, and $2k>n$.The proof combines a concavity inequality with a pointwise doubling argument.