Lecture Hall 5F, Cosmology Building, NTU

(臺灣大學宇宙學大樓 五樓演講廳)

Generic Singularities of the Network Flow

Jui-En Chang (National Taiwan University)

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 networks 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 finitely many of them and they are completely classified. 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.