On the propagation of singularities of constant curvature, convex hypersurfaces

TL;DR

This paper investigates the structure of singularities in convex hypersurfaces of constant curvature within hyperbolic space and applies these findings to the ideal Plateau problem for such surfaces.

Contribution

It characterizes the singular sets of convex hypersurfaces with constant curvature in hyperbolic space for general convex curvature functions and explores their implications for the Plateau problem.

Findings

Describes the structure of singular sets in these hypersurfaces.

Provides insights into the ideal Plateau problem in hyperbolic space.

Extends understanding of curvature and singularities in geometric analysis.

Abstract

We describe the structure of the singular sets of constant curvature, convex hypersurfaces in hyperbolic space for general convex curvature functions. We apply this result to the study of the ideal Plateau problem in hyperbolic space for such curvature functions.