The wetted solid - a generalization of Plateau's problem and its implications for sintered materials

We introduce a new generalization of the Plateau problem which includes the constraint of enclosing a given region. Physically the problem is important insofar as it bears on sintering processes and on the structure of wetted porous media. Some primal and dual characterizations of the solutions are offered, and aspects of the problem are illustrated in one and two dimensions in order to clarify the combinatorial elements and to demonstrate the importance of numerous local minima. (orig.)