A Brief Note on Foliations of Constant Gaussian Curvature

TL;DR

This paper offers an alternative proof that the complements of the convex core in certain hyperbolic 3-manifolds can be foliated by hypersurfaces of constant Gaussian curvature, enriching the understanding of their geometric structure.

Contribution

It provides a new proof of Labourie's result on foliations of hyperbolic 3-manifolds, expanding the theoretical framework of geometric structures in hyperbolic geometry.

Findings

Complement regions are foliated by constant Gaussian curvature hypersurfaces

The proof offers a new perspective on Labourie's original result

Enhances understanding of geometric structures in hyperbolic 3-manifolds

Abstract

This note provides an alternative proof of a result of Labourie. We show that the two complements of the convex core of a three dimensional quasi-fuchsian hyperbolic manifold may be foliated by embedded hypersurfaces of constant Gaussian curvature.