Hypersurfaces of Constant Curvature in Hyperbolic Space I

TL;DR

This paper studies the existence of complete, strictly convex hypersurfaces with constant curvature in hyperbolic space, focusing on those with a specified boundary at infinity for various curvature functions.

Contribution

It introduces a general framework for constructing such hypersurfaces with prescribed asymptotic boundaries in hyperbolic space.

Findings

Established existence results for hypersurfaces with constant curvature

Extended methods to a broad class of curvature functions

Provided new insights into boundary behavior at infinity

Abstract

We investigate the problem of finding complete strictly convex hypersurfaces of constant curvature in hyperbolic space with a prescribed asymptotic boundary at infinity for a general class of curvature functions.