论文标题
分裂基本亚组的双曲线组的共形尺寸
Conformal dimension of hyperbolic groups that split over elementary subgroups
论文作者
论文摘要
我们研究了在基本亚组分裂的Gromov双曲线基团无穷大的边界的（AHLFORS常规）保形维度。如果该组几乎不是自由的，我们表明保形维度等于顶点组的共形维度的最大值，或1，以更大为准，并且当达成共形维度时表征。结果，我们能够表征哪些Gromov双曲线群（没有$ 2 $ torsion）具有共形维度1，并回答了Bonk和Kleiner的问题。
We study the (Ahlfors regular) conformal dimension of the boundary at infinity of Gromov hyperbolic groups which split over elementary subgroups. If such a group is not virtually free, we show that the conformal dimension is equal to the maximal value of the conformal dimension of the vertex groups, or 1, whichever is greater, and we characterise when the conformal dimension is attained. As a consequence, we are able to characterise which Gromov hyperbolic groups (without $2$-torsion) have conformal dimension 1, answering a question of Bonk and Kleiner.
