Interior Hessian estimates for Hessian quotient equations in dimension three

Heming Jiao, Zhenan Sui

In this paper, we establish the interior Hessian estimates for $2$-convex solutions to $\frac{{\sigma }_2}{{\sigma }_1}(D^{2}u)=\psi (x,u)$ in dimension three. In higher dimensions ($n\ge 4$), we…