8 problems

Fix $m$ and consider harmonic maps from domains in $\mathbb{R}^m$ into a tree. For a homogeneous map, let $\alpha\geq 1$ denote its order. Consider finitely many open domains…

Let $(r_1,\dots,r_k)$ be a sequence of non-negative real numbers satisfying … so that $(r_1,\dots,r_k)$ is convex. Let $T$ be a metric tree with total length…

Let $r>0$, let $T$ be a metric tree with total length $|T|\geq 2r$, and let $\mathcal{C}(T,0)$ denote the relevant space of covers of $T$ by radius-zero centers. Let $E\nu$ denote…

Let $X$ be a metric space and let $Q_o=[0,1]^3$. A Lipschitz map $f\colon Q_o\to X$ is said to factor through a metric tree if there are Lipschitz maps $\psi\colon Q_o\to Z$ and…

Let $\mathcal G$ be a rooted or non-rooted binary metric tree with Kirchhoff vertex conditions, and let $\mathcal L_{\mathcal G}(m)$ be the minimum of the Schrödinger energy at fix…

Let $\mathcal G$ be a rooted or non-rooted binary metric tree with Kirchhoff vertex conditions, and let $M(u)=m$ denote fixed mass. For a mass-subcritical power nonlinearity…

Let $T$ be a finite metric tree, and let $n$ be a positive integer. The tree $T$ has at most $2^n$ leaves. An isometric embedding of $T$ into $(\mathbb{R}^n,d_{\infty})$ is a map p…

Let $({\bf X},\lambda)$ be a locally finite metric tree without terminal vertices, let $X=|{\bf X}|_\lambda$ be its geometric realisation, and let $\Gamma$ be a nonelementary discr…