Harmonic maps and constant mean curvature surfaces in H 2 x R

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...

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

Constant mean curvature surfaces and integrable equations