论文标题
任意有限生成的缩放组的度量空间
Metric Spaces of Arbitrary Finitely-Generated Scaling Group
论文作者
论文摘要
对于标准空间$ x $，带有兼容度量$μ$的$ $ $，Genevois和Tessera将$（x，μ）$的比例定义为$ \ mathbb {r} _ {r} _ {r} _ {> 0} $ $ x $ $ x $ coarsy $ c $ x $ c $ x $ us的$ \ mathbb {r} _ {> 0} $ a a $ x $ a a的$ umeTial $ c。我们表明，对于任何有限生成的子组$γ$ $ \ mathbb {r} _ {> 0} $，存在一个空间$n_γ$，bi-lipschitz，等效于有限程度，并带有缩放组$γ$。
For a metric space $X$ with a compatible measure $μ$, Genevois and Tessera defined the Scaling Group of $(X,μ)$ as the subgroup $Γ$ of $\mathbb{R}_{>0}$ of positive real numbers $γ$ for which there are quasi-isometries of $X$ coarsely scaling $μ$ by a factor of $γ$. We show that for any finitely generated subgroup $Γ$ of $\mathbb{R}_{>0}$ there exists a space $N_Γ$, bi-Lipschitz equivalent to a graph of finite degree, with scaling group $Γ$.
