6 problems

Let $\boldsymbol{D}_0$ be embedded in $\boldsymbol{D}$ under the setting of Proposition, and let $\mathcal M^{\alpha}$ denote the Hausdorff measure used in that setting. Embedded-s…

Let $\boldsymbol{D}$ be the random metric object in the unimodular Frostman setting, let $\mathcal H^{\alpha}_{M}(\boldsymbol{D})$ denote its unimodular Hausdorff measure, and let…

Let $\boldsymbol{D}$ be the object considered in the paper, with $\mathrm{{udim}}_H(\boldsymbol{D})$ denoting its unimodular Hausdorff dimension. Call the underlying setting non-am…

Let $[\boldsymbol{T},\boldsymbol{o}]$ be a unimodular eternal Galton–Watson tree. Suppose its offspring distribution is in the domain of attraction of an $\alpha$-stable distributi…

Let $T_3$ be the 3-regular tree, and let $\boldsymbol{d}'$ be an equivariant metric, meaning a metric satisfying the equivariance condition from Definition. 3-regular-tree conjectu…

Let $[\boldsymbol{T},\boldsymbol{o}]$ be a unimodular tree with infinitely many ends, endowed with its graph-distance metric. Infinite-dimensionality conjecture. One has … This is…