Radial graphs of constant mean curvature and doubly connected minimal surfaces with prescribed boundary

In this paper we investigate existence and uniqueness of radial graphs of constant mean curvature (cmc) with prescribed boundary. Our main result establishes the existence of a minimal radial anullus spanning two given convex curves in parallel planes of R-3; we also obtain a variant of a well-known result of James Serrin about the existence of radial cmc graphs over convex domains in the sphere.