DATE2021-10-07 16:10-17:00



TITLEStability of Regular Shrinkers in the Network Flow

ABSTRACT In this talk, I'll present the problem I'm working on and some partial results. In the network flow, singularities may form. They can be described as self-similar shrinking solutions called regular shrinkers. An important problem is that if we perturb the initial network, will the new network flow to the same singularity? All network with 2 or more enclosed regions can be perturbed away. Therefore, the problem reduces to the network with less than 2 enclosed regions. There are infinitely many of them and they are completely classifi ed. Here, I use the entropy argument as in Colding and Minicozzi's work to show that the 4-ray star, the 5-ray star, the fish, and the rocket can be perturbed away.