GEOMETRY AND FOAMS - 2D DYNAMICS AND 3D STATICS

We discuss the implications of the classical Gauss-Bonnet formula to foam in two and three dimensions. For a two-dimensional foam it gives a generalization of the von Neumann law for the coarsening of foams to curved surfaces. As a consequence of this we find that the stability properties of stationary bubbles of such a froth depend on the Gaussian curvature of the surface. For three-dimensional foam we find a relation between the average Gaussian curvature of a soap film and the average number of vertices for each face.