This paper is devoted primarily to the study of properties of the Grassmannian of oriented 2-planes in [double-struck capital]ℝ[superscript]n and to applications of these properties to understanding minimal surfaces in [double-struck capital]ℝ[superscript]n via the generalized G…
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 …
