Abstract:

The network flow is a generalization of the curve shortening flow from curves to planar networks. To study the formation of singularities, solutions which move by homothety scaling plays an important role. Such network is called a regular shrinker. Up to now, only the shrinker with less than 2 triple junctions or 1 closed region is classified. In this talk, I'll present our recent result about the classification of regular shrinker with 2 closed regions. This is a joint work with Dr. Yang-Kai Lue.