An iterative process in the problem of plateau

be small. The boundary conditions were also replaced by approximate conditions. I gave a direct construction for the approximate solutions; the exact solution was then obtained by a passage to the limit. The main purpose of the present paper is to develop an iterative process which produces automatically a sequence of approximate solutions. The idea of the process (described and discussed in ?2) is to comply with the above conditions (I) and (II) alternately. The process starts with an arbitrary harmonic surface bounded by the given curve and thus the result depends, in general, upon the choice of this initial harmonic surface. In this sense, the process contains an arbitrary parameter, namely the initial harmonic surface ID o, and this fact accounts for the great flexibility of the method.