Research reveals existence of smooth complete hypersurfaces with constant curvature, indicating broader curvature applicability.
In this note, we investigate the existence of smooth complete hypersurfaces in hyperbolic space with constant curvature and a prescribed asymptotic boundary at infinity. By deriving curvature estimates, we are able to deduce the existence in some cases. Previously, these existence results were proved for a restricted range of curvature values, while here we prove the existence for all possible curvature values.
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Bin Wang (2025) studied this question.
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