Stability of surfaces with constant mean curvature bounded by two coaxial circles

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, ...

Surfaces of Constant Mean Curvature Bounded by Two Planar Curves ? RAFAEL LÓPEZ

In this paper we study constant mean curvature compact surfaces with two Jordan curves in parallel planes as boundary and we investigate the point at which the surface inherits the symmetries of its boundary.

Stability and Bifurcation for Surfaces with Constant Mean Curvature

We give criteria for the existence of smooth bifurcation branches of fixed boundary CMC surfaces in R, and we discuss stability/instability issues for the surfaces in bifurcating branches. To illustrate the theory, we discuss an explicit example obtained from a bifurcating branch of fixed boundary unduloids inR.

Surfaces of Constant Mean Curvature

Constant Mean Curvature Surfaces with Two Ends in Hyperbolic Space

We investigate the close relationship between minimal surfaces in Euclidean 3-space and constant mean curvature 1 surfaces in hyperbolic 3-space. Just as in the case of minimal surfaces in Euclidean 3-space, the only complete connected embedded constant mean curvature 1 surfaces with two ends in hyperbolic space are well-understood surfaces of revolution – the catenoid cousins. In contrast to t...