Non-properly Embedded Minimal Planes in Hyperbolic 3-Space
Differential Geometry
2015-03-17 v1 Geometric Topology
Abstract
In this paper, we show that there are non-properly embedded minimal surfaces with finite topology in a simply connected Riemannian 3-manifold with nonpositive curvature. We show this result by constructing a non-properly embedded minimal plane in hyperbolic 3-space. Hence, this gives a counterexample to Calabi-Yau conjecture for embedded minimal surfaces in the negative curvature case.
Cite
@article{arxiv.1101.3843,
title = {Non-properly Embedded Minimal Planes in Hyperbolic 3-Space},
author = {Baris Coskunuzer},
journal= {arXiv preprint arXiv:1101.3843},
year = {2015}
}