The question of Plateau concerns the existences soap films: objects of minimial area spanning a given curve in the Euclidean spaces. The most classical answer to this question has been provided by Rado and Douglas and proves the existence of parametrized discs of minimal area spanning an arbitrary Jordan curve. The result was generalized by Morrey to Riemannian manifolds. In the talk I will discuss a solution of the Plateau problem in arbitrary metric spaces, regularity of the solutions and some applications to isoperimetric problems.
