6 problems

Let $\Gamma$ be a surface group acting by isometries on an $\mathbb R$-tree. The action is minimal if no proper subtree is invariant under $\Gamma$, and small if edge stabilizer su…

Berestovskis conjecture. The space $X$ is homeomorphic to the topological product

Let $\Gamma$ be a hyperbolic group acting isometrically on an $\mathbb{R}$-tree. The associated stable translation length function is the function assigning to each element its sta…

Generalization conjecture. The assumption that $X$ is locally compact can be dropped from the theorem asserting that every Lipschitz map from a closed subset of $X$ to a metric tre…

Swenson's conjecture. The regular big tree $T$ is an $\mathbb{R}$-tree.

Let $T\in\partial cv_N$ be an $\mathbb R$-tree with dense orbits, and suppose that its dual lamination $L(T)$ is uniquely ergodic; then $T$ is dually uniquely ergodic. In this case…