Darboux transforms and simple factor dressing of constant mean curvature surfaces

Discrete surfaces of constant mean curvature via dressing

We start in Section 2 with the definition of the discrete (standard) cylinder as an example of a discrete CMC-surface in the sense of Bobenko and Pinkall [3, 4] (Definition 2.4). This will also lead to the introduction of so called extended frames for discrete CMC-surfaces. These definitions will describe the discrete analogues of CMC-surfaces without umbilics in an isothermic parametrization. ...

Surfaces of Constant Mean Curvature

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...

Constant mean curvature surfaces and integrable equations