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Abstract 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.
Jiao et al. (Fri,) studied this question.