# Non-properly Embedded H-Planes in Hyperbolic 3-Space

@article{Coskunuzer2015NonproperlyEH, title={Non-properly Embedded H-Planes in Hyperbolic 3-Space}, author={Baris Coskunuzer and William H. Iii Meeks and Giuseppe Tinaglia}, journal={arXiv: Differential Geometry}, year={2015} }

For any H in [0,1), we construct complete, non-proper, stable, simply-connected surfaces with constant mean curvature H embedded in hyperbolic 3-space.

## 5 Citations

Asymptotic H-Plateau Problem in Hyperbolic 3-space

- Mathematics
- 2015

We show that if a Jordan curve C in the asymptotic sphere contains a smooth point, there is an embedded H-plane in H^3 asymptotic to C for any H in [0,1).

H-Surfaces with Arbitrary Topology in Hyperbolic 3-Space

- Mathematics
- 2017

We show that any open orientable surface can be properly embedded in $$\mathbb {H}^3$$H3 as a constant mean curvature H-surface for $$H\in [0,1)$$H∈[0,1). We obtain this result by proving a version…

Non-properly embedded H-planes in $${\mathbb H}^2\times {\mathbb R}$$H2×R

- Mathematics
- 2018

For any $$H \in (0,\frac{1}{2})$$H∈(0,12), we construct complete, non-proper, stable, simply-connected surfaces embedded in $${\mathbb H}^2\times {\mathbb R}$$H2×R with constant mean curvature H.

The geometry of constant mean curvature surfaces in $\mathbb{R}^3$

- Mathematics
- 2016

We derive intrinsic curvature and radius estimates for compact disks embedded in $\mathbb{R}^3$ with nonzero constant mean curvature and apply these estimates to study the global geometry of complete…

Asymptotic H–Plateau problem in ℍ3

- Mathematics
- 2016

There are two versions of the asymptotic Plateau problem. The first version asks the existence of a least area plane P in H asymptotic to a given simple closed in S 1.H /, ie @1PD . In this…

## References

SHOWING 1-10 OF 12 REFERENCES

NON-PROPERLY EMBEDDED MINIMAL PLANES IN HYPERBOLIC 3-SPACE

- Mathematics
- 2011

In this paper, we show that there are non-properly embedded minimal surfaces with finite topology in a simply connected Riemannian 3-manifold with non-positive curvature. We show this result by…

Least Area Planes in Hyperbolic 3-space Are Properly Embedded

- Mathematics
- 2009

We show that if Σ is an embedded least area (area minimizing) plane in H 3 whose asymptotic boundary is a simple closed curve with at least one smooth point, then Σ is properly embedded in H 3 .

General curvature estimates for stable H-surfaces in 3-manifolds applications

- Mathematics
- 2009

We obtain an estimate for the norm of the second fundamental form of stable H-surfaces in Riemannian 3-manifolds with bounded sectional curvature. Our estimate depends on the distance to the boundary…

Topological Type of Limit Laminations of Embedded Minimal Disks

- Mathematics
- 2013

We consider two natural classes of minimal laminations in three-manifolds. Both classes may be thought of as limits - in different senses - of embedded minimal disks. In both cases, we prove that,…

Existence an regularity of constant mean curvature hypersurfaces in hyperbolic space

- Mathematics
- 1996

Non-proper complete minimal surfaces embedded in H^2 x R

- Mathematics
- 2012

Examples of complete minimal surfaces properly embedded in H^2 x R have been extensively studied and the literature contains a plethora of nontrivial ones. In this paper we construct a large class of…

Some remarks on the existence of hypersurfaces of constant mean curvature with a given boundary, or asymptotic boundary, in hyperbolic space

- Mathematics
- 1997

In this paper we will describe situations where we can find two solutions. For example, if Γ is on a sphere of radius R, then there are two H-surfaces in the ball bounded by the sphere (with boundary…

The minimal lamination closure theorem

- Mathematics
- 2006

We prove that the closure of a complete embedded minimal surface M in a Riemannian three-manifold N has the structure of a minimal lamination, when M has positive injectivity radius. When N is R, we…

The Calabi-Yau conjectures for embedded surfaces

- Mathematics
- 2004

In this talk I will discuss the proof of the Calabi-Yau conjectures for embedded surfaces. This is joint work with Bill Minicozzi, [CM9]. The Calabi-Yau conjectures about surfaces date back to the…