On the Problem of Plateau Subharmonic Functions A convex function f may be called sublinear in the following sense; if a linear function l is ::=: j at the boundary points of an interval then l:> j in the interior of that interval also. If we replace the terms interval and linear junction by the terms domain and harmonic function we obtain a statement which expresses the characteristic property of subharmonic functions of two or more variables. This ge­ neralization formulated and developed by F. RIEsz immediately at­ tracted the attention of many mathematicians both on account of its intrinsic interest and on account of the wide range of its applications. If f (z) is an analytic function of the complex variable z = x + i y. then If (z) I is subharmonic. The potential of a negative mass distribu­ tion is subharmonic. In differential geometry surfaces of negative curvature and minimal surfaces can be characterized in terms of sub­ harmonic functions. The idea of a subharmonic function leads to significant applications and interpretations in the fields just referred to and· conversely every one of these fields is an apparently in­ exhaustible source of new theorems on subharmonic functions either by analogy or by direct implication. I. Curves and surfaces II. Minimal surfaces in the small III Minimal surfaces in the large IV. The non parametric problem V. The problem of Plateau in the parametric form VI. The simultaneous problem in the parametric form. Generalizations I. Definition and preliminary discussion II. Integral means III. Criterions and constructions IV. Examples V. Harmonic majorants VI. Representation in terms of potentials VII. Analogies between harmonic and subharmonic functions References.