The Pogorelov Estimates for Degenerate Curvature Equations.

We establish the Pogorelov-type estimates for degenerate prescribed |$k$| -curvature equations as well as |$k$| -Hessian equations. Furthermore, we investigate the interior |$C^{1,1}$| regularity of the solutions for Dirichlet problems. These techniques also enable us to improve the existence theorem for an asymptotic Plateau-type problem in hyperbolic space. [ABSTRACT FROM AUTHOR]