More on the Determinacy of Smooth Map-Germs.
We consider the motion by curvature of a network of smooth curves with multiple junctions in the plane, that is, the geometric gradient flow associated to the length functional. Such a flow represents the evolution of a two–dimensional multiphase system where the energy is simply the sum of the lengths of the interfaces, in particular it is a possible model for the growth of grain boundaries. Moreover, the motion of these networks of curves is the simplest example of curvature flow for sets which...