Asymptotically Poincar\'e surfaces in quasi-Fuchsian manifolds
Differential Geometry
2019-08-02 v2
Abstract
We introduce the notion of an asymptotically Poincar\'e family of surfaces in an end of a quasi-Fuchsian manifold. We show that any such family gives a foliation of an end by asymptotically parallel convex surfaces, and that the asymptotic behavior of the first and second fundamental forms determines the projective structure at infinity. As an application, we establish a conjecture of Labourie from 1992 regarding constant Gaussian curvature surfaces. We also derive consequences for constant mean curvature surfaces.
Keywords
Cite
@article{arxiv.1811.08828,
title = {Asymptotically Poincar\'e surfaces in quasi-Fuchsian manifolds},
author = {Keaton Quinn},
journal= {arXiv preprint arXiv:1811.08828},
year = {2019}
}
Comments
Slight improvement to main theorems. Other small changes based on referee's report