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

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

Categories: math.AP math.DG