Some strange properties of minimal surfaces in connection with Plateau's problem

In this paper we shall prove the existence of some minimal surfaces passing through enough smooth curves, surfaces which satisfy some given boundary conditions. We shall point out a strange property of ‘cutting’ of these surfaces, at least for large classes of curves and boundary conditions. The theoretical results will be completed, on the one hand, by a graphical study, to construct and to see the surfaces, and on the other hand, by a numerical study, to obtain the geometry of the cuts.