We establish the Pogorelov-type estimates for degenerate prescribed k-curvature equations as well as k-Hessian equations. Furthermore, we investigate the interior C1,1 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.
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Jiao et al. (2024) studied this question.
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