On the Classification of Networks Self–Similarly Moving by Curvature
We give an overview of the classification of networks in the plane with at most two triple junctions with the property that under the motion by curvature they are self-similarly shrinking. After the contributions in [7, 9, 20], such a classification was completed in the recent work in  (see also ), proving that there are no self-shrinking networks homeomorphic to the Greek “theta” letter (a double cell) embedded in the plane with two triple junctions with angles of 120 degrees. We present the main geometric ideas behind the work . We also briefly introduce our work in progress in the higher-dimensional case of networks of surfaces in R3.