Constant mean curvature surfaces of annular type

Abstract.

We consider large solutions of annular type to the volume constrained Douglas problem. They are conformally immersed H-surfaces. By rescaling we set the volume functional at one while the boundary curves shrink to the origin. We show that the solutions become spherical in a precise manner. Spherical bubbling may fail if the conformality condition is dropped. We also discuss the rotationally symmetric annular solutions to the H-surface equation and consider some illustrative examples.