Coarse classification of constant mean curvature cylinders

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Surfaces of Constant Mean Curvature

On the Moduli of Constant Mean Curvature Cylinders of Finite Type in the 3-sphere

We show that one-sided Alexandrov embedded constant mean curvature cylinders of finite type in the 3-sphere have spectral genus g ≤ 1. This confirms a conjecture by Pinkall and Sterling that the only embedded constant mean curvature tori in the 3-sphere are tori of revolution.

New Constant Mean Curvature Surfaces

We use the DPW construction [5] to present three new classes of immersed CMC cylinders, each of which includes surfaces with umbilics. The first class consists of cylinders with one end asymptotic to a Delaunay surface. The second class presents surfaces with a closed planar geodesic. In the third class each surface has a closed curve of points with a common tangent plane. An appendix, by the t...

Coplanar Constant Mean Curvature Surfaces

We consider constant mean curvature surfaces with finite topology, properly embedded in three-space in the sense of Alexandrov. Such surfaces with three ends and genus zero were constructed and completely classified by the authors [GKS2, GKS1]. Here we extend the arguments to the case of an arbitrary number of ends, under the assumption that the asymptotic axes of the ends lie in a common plane...