This memoir is devoted to the case of constant mean curvature surfaces immersed in [bold]R³. We reduce this geometrical problem to finding certain integrable solutions to the Gauss equation. Many new and interesting examples are presented, including immersed cylinders in [bold]R…
The classical problem of Plateau is studied from the point of view of global nonlinear analysis. It is shown that minimal surfaces of the topological type of the two disc arise as the zeros of a Fredholm vector field on an infinite dimensional manifold. A framework is developed …
In this paper we formulate and prove an index theorem for minimal surfaces of higher topological type spanning one boundary contour. Our techniques carry over to surfaces with several boundary contours as well as to unoriented surfaces.
