Surfaces of constant mean curvature in manifolds of constant curvature

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...

Polyhedral Surfaces of Constant Mean Curvature

way, say, by assigning a length to each edge which fulÞlls the triangle identity on each triangle. In a locally Euclidean metric the distance between two points is measured along curves whose length is measured segment-wise on the open edges and triangles: DeÞnition 15 A curve γ on a simplicial complex M is called rectiÞable, if for every simplex σ ∈ M the part γ|σ is rectiÞable w.r.t. to the s...

Delaunay Ends of Constant Mean Curvature Surfaces

We use the generalized Weierstrass representation to analyze the asymptotic behavior of a constant mean curvature surface that locally arises from an ODE with a regular singularity. We show that if system is a perturbation of that of a Delaunay surface, then the corresponding constant mean curvature surface has a properly immersed end that is asymptotically Delaunay. Furthermore, that end is em...