论文标题
圆树和随机组中的共形尺寸：低密度至高密度
Round Trees and Conformal Dimension in Random Groups: low density to high density
论文作者
论文摘要
我们研究了Gromov密度模型$ \ MATHCAL {g}^d_ {m，l} $ a $ m \ geq 2 $固定发电机，密度$ 0 <d <1/2 $和relator length Lengthe $ l \ f to \ fty fty $ ftty $。我们的主要结果是所有密度的$ l $中的下边线线性$ 0 <d <1/2 $，通过建造直接来自较低密度的gromov随机组而实现的未呈现的圆形树。
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.
