The Topology of constant mean curvature surfaces with convex bundary

Author: B. Nelli

Abstract: We discuss old and new results about the shape of a constant mean curvature surface, with convex boundary, contained in one of the halfspaces determined by the plane containing the boundary. The ambient manifold will be either \({\mathbb R}^3\) or \({\mathbb H}^2\times{\mathbb R}\). The talk is based on a joint work with G. Pipoli.