Convex Hypersurfaces with Prescribed Scalar Curvature and Asymptotic Boundary in Hyperbolic Space

TL;DR

This paper proves the existence of smooth, convex hypersurfaces in hyperbolic space with specified scalar curvature and boundary at infinity, assuming a suitable subsolution exists.

Contribution

It establishes the existence of such hypersurfaces in hyperbolic space under new conditions involving subsolutions.

Findings

Existence of convex hypersurfaces with prescribed scalar curvature in hyperbolic space.

Construction of solutions assuming the existence of a subsolution.

Advancement in geometric analysis of hypersurfaces in hyperbolic space.

Abstract

The existence of a smooth complete strictly locally convex hypersurface with prescribed scalar curvature and asymptotic boundary at infinity in $\mathbb{H}^{3}$ is proved under the assumption that there exists a strictly locally convex subsolution.