• Corpus ID: 119639350

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. 
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References

SHOWING 1-10 OF 12 REFERENCES
NON-PROPERLY EMBEDDED MINIMAL PLANES IN HYPERBOLIC 3-SPACE
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
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