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Round Trees and Conformal Dimension in Random Groups: low density to high density

· 2022 · math.GR · arXiv 2204.05165

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abstract

We investigate conformal dimension for the class of infinite hyperbolic groups in the Gromov density model $\mathcal{G}^d_{m,l}$ of random groups with $m \geq 2$ fixed generators, density $0 < d < 1/2$ and relator length $l \to \infty$. Our main result is a lower bound linear in $l$ at all densities $0 < d < 1/2$ achieved by building undistorted round trees coming directly from lower density Gromov random groups.

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  • Visual metrics on boundaries of hyperbolic spaces math.GT · 2025-06-11 · conditional · none · ref 2003 · internal anchor

    An expository article on visual metrics on boundaries of hyperbolic spaces, quasisymmetries, conformal dimension, and round trees.