Cylindrically bounded constant mean curvature surfaces in $\mathbb {H} ^2\times \mathbb {R}$

Surfaces of Constant Mean Curvature Bounded by Convex Curves

This paper proves that an embedded compact surface in the Euclidean space with constant mean curvature H 6= 0 bounded by a circle of radius 1 and included in a slab of width 1=jHj is a spherical cap. Also, we give partial answers to the problem when a surface with constant mean curvature and planar boundary lies in one of the halfspaces determined by the plane containing the boundary, exactly, ...

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...

Surfaces of Constant Mean Curvature

Deformations of constant mean curvature 1/2 surfaces in H × R with vertical ends at infinity

We study constant mean curvature 1/2 surfaces in H × R that admit a compactification of the mean curvature operator. We show that a particular family of complete entire graphs over H admits a structure of infinite dimensional manifold with local control on the behaviors at infinity. These graphs also appear to have a half-space property and we deduce a uniqueness result at infinity. Deforming n...