Embedded $H$-Planes in Hyperbolic 3-Space
Differential Geometry
2019-06-04 v1 Geometric Topology
Abstract
We show that for any C^0 Jordan curve C in the sphere at infinity of H^3, there exists an embedded -plane P_H in H^3 with asymptotic boundary C for any H in (-1,1). As a corollary, we proved that any quasi-Fuchsian hyperbolic 3-manifold M=SxR contains an H-surface S_H in the homotopy class of the core surface S for any H in (-1,1). We also proved that for any C^1 Jordan curve J in the sphere at infinity, there exists a unique minimizing H-plane P_H with asymptotic boundary J for a generic H in (-1,1).
Cite
@article{arxiv.1705.02951,
title = {Embedded $H$-Planes in Hyperbolic 3-Space},
author = {Baris Coskunuzer},
journal= {arXiv preprint arXiv:1705.02951},
year = {2019}
}
Comments
21 pages, 3 figures