Curvature estimates for hypersurfaces of constant curvature in hyperbolic space II

TL;DR

This paper proves the existence of smooth complete hypersurfaces with constant -curvature in hyperbolic space for all curvature values by deriving new curvature estimates.

Contribution

It extends previous results by establishing existence for all possible curvature values through novel curvature estimates.

Findings

Existence of hypersurfaces with constant -curvature for all values

Derived curvature estimates enable the existence proof

Addresses previously restricted curvature range

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.