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In this paper, we consider the asymptotic ₖ Plateau problem in hyperbolic space. We establish C² estimates for semi-convex complete hypersurfaces satisfying constant ₖ curvature with a prescribed asymptotic boundary at the infinity for 2 k n-2. The result is based on a new crucial concavity inequality derived for hessian equations.
Han et al. (Sun,) studied this question.