Pogorelov type estimates for a class of Hessian quotient equations in Lorentz-Minkowski space [formula omitted

Abstract

Let Ω be a bounded domain (with smooth boundary) on the hyperbolic plane Hn(1), of center at origin and radius 1, in the (n+1)-dimensional Lorentz-Minkowski space R1n+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 Ω⊂Hn(1) and with the vanishing Dirichlet boundary condition.