An existence theorem for surfaces of constant mean curvature

A general halfspace theorem for constant mean curvature surfaces

In this paper, we prove a general halfspace theorem for constant mean curvature surfaces. Under certain hypotheses, we prove that, in an ambient space M, any constant mean curvature H0 surface on one side of a constant mean curvature H0 surface Σ0 is an equidistant surface to Σ0. The main hypotheses of the theorem are that Σ0 is parabolic and the mean curvature of the equidistant surfaces to Σ0...

Surfaces of Constant Mean Curvature

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.

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...