In this paper, we consider the asymptotic σₖ Plateau problem in hyperbolic space. We establish C² estimates for semi-convex complete hypersurfaces satisfying constant σₖ 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.
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Han et al. (2024) studied this question.
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