Pogorelov type estimates for a class of Hessian quotient equations in Lorentz-Minkowski space ${\mathbb{R}}_1^{n+1}$

Abstract

Let $\Omega$ be a bounded domain (with smooth boundary) on the hyperbolic plane ${\mathcal{H}}^n(1)$, of center at origin and radius $1$, in the $(n+1)$-dimensional Lorentz-Minkowski space ${\mathbb{R}}_1^{n+1}$. 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 $\Omega \subset {\mathcal{H}}^n(1)$ and with the vanishing Dirichlet boundary condition.

13 pages. We have corrected a mistake in the proof of main theorem of the previous version v1 and we have also simplified the proof a lot. Besdies, several new references have been added. Comments are welcome