Curvature estimates for hypersurfaces of constant curvature in hyperbolic space II

Abstract

In this note, we investigate the existence of smooth complete hypersurfaces in hyperbolic space with constant $(n-2)$-curvature and a prescribed asymptotic boundary at infinity. Previously, the existence was known only for a restricted range of curvature values, while in here, by deriving curvature estimates, we are able to deduce the existence for all possible curvature values.