Hypersurfaces of Constant Curvature in Hyperbolic Space II

TL;DR

This paper constructs complete hypersurfaces with constant curvature in hyperbolic space, matching prescribed boundary conditions at infinity for a broad class of curvature functions, including higher order mean curvatures.

Contribution

It extends the existence results of constant curvature hypersurfaces in hyperbolic space to a general class of elliptic curvature functions with prescribed asymptotic boundaries.

Findings

Existence of hypersurfaces with prescribed boundary at infinity.

Applicable to a wide class of elliptic curvature functions.

Includes higher order mean curvatures and their quotients.

Abstract

We find complete hypersurfaces of constant curvature in hyperbolic space with a prescribed asymptotic boundary at infinity for a general class of (elliptic) curvature functions which includes the higher order mean curvatures and their curvature quotients.