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Let $\Omega$ be a bounded domain (with smooth boundary) on the hyperbolicplane $\mathscr{H}^{n}(1)$, of center at origin and radius $1$, in the$(n+1)$-dimensional Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$. In thispaper, by using a priori estimates, we can establish Pogorelov type estimatesof $k$-convex solutions to a class of Hessian quotient equations defined over$\Omega\subset\mathscr{H}^{n}(1)$ and with the vanishing Dirichlet boundarycondition.

Pogorelov type estimates for a class of Hessian quotient equations in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$