Pogorelov type interior $C^2$ estimate for Hessian quotient equation and its application

Siyuan Lu, Yi-Lin Tsai

In this paper, we derive a Pogorelov type interior $C^2$ estimate for the Hessian quotient equation $\frac{{\sigma }_n}{{\sigma }_k}\left(D^{2}u\right)=f$. As an application, we show that convex v…