• Corpus ID: 119639350

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

  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},
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

Figures from this paper

Asymptotic H-Plateau Problem in Hyperbolic 3-space
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
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
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 $\mathbb{R}^3$
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
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


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
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
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
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,
Non-proper complete minimal surfaces embedded in H^2 x R
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
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
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
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
Spherical surfaces with constant mean curvature in hyperbolic space