Singularities of the network flow with symmetric initial data

TL;DR

This paper investigates the development of singularities in network curvature flow with symmetric initial data, demonstrating that such flows only develop finitely many singularities when starting with symmetric configurations involving two triple junctions.

Contribution

It establishes the finiteness of singular times for symmetric network flows with specific initial configurations, advancing understanding of singularity formation in curvature flows.

Findings

Finite number of singular times for symmetric initial data

Symmetry conditions influence singularity development

Results applicable to networks with two triple junctions

Abstract

We study the formation of singularities for the curvature flow of networks when the initial data is symmetric with respect to a pair of perpendicular axes and has two triple junctions. We show that, in this case, the set of singular times is finite.