3 problems

Consider the evolution of a tree under network flow. A singular time is a time at which the flow develops a singularity, and a boundary curve is a curve of the network ending at th…

Let $\mathcal{G}^n$ be the class of embedded graphs in $\mathbb{R}^n$. Suppose $G\in\mathcal{G}^n$ is an embedded graph with a homogeneous topological cloth and a well-defined time…

Let $\mathcal{G}^n$ denote the class of embedded graphs in $\mathbb{R}^n$, and let a network flow $G(t)$ have homogeneous initial condition $G(0)\in\mathcal{G}^n$. Let $\sigma_n$ b…