Constant mean curvature surfaces of Delaunay type along a closed geodesic

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...

Constant mean curvature surfaces with Delaunay ends

In this paper we shall present a construction of Alexandrov-embedded complete surfaces M in R with nitely many ends and nite topology, and with nonzero constant mean curvature (CMC). This construction is parallel to the well-known original construction by Kapouleas [3], but we feel that ours somewhat simpler analytically, and controls the resulting geometry more closely. On the other hand, the ...

Aleksandrov’s Theorem: Closed Surfaces with Constant Mean Curvature

We present Aleksandrov’s proof that the only connected, closed, ndimensional C hypersurfaces (in R) of constant mean curvature are the spheres.

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...