论文标题
统一的树枝
Uniformly branching trees
论文作者
论文摘要
准文化树$ t $是一棵（紧凑的）公制树，它正在加倍且有限的转弯。如果$ t $的每个分支机点都有三个分支，我们将称为$ t $三价。如果一组分支点相对分离，并且相对密度均匀，我们说$ t $是统一的分支。我们证明，当且仅当它是一条均匀分支的三价准形式树时，且仅当它是一个三价的准形式树时，公制空间$ t $与连续的自相似树相对。特别是，这种类型的任何两棵树都是准对称等效的。
A quasiconformal tree $T$ is a (compact) metric tree that is doubling and of bounded turning. We call $T$ trivalent if every branch point of $T$ has exactly three branches. If the set of branch points is uniformly relatively separated and uniformly relatively dense, we say that $T$ is uniformly branching. We prove that a metric space $T$ is quasisymmetrically equivalent to the continuum self-similar tree if and only if it is a trivalent quasiconformal tree that is uniformly branching. In particular, any two trees of this type are quasisymmetrically equivalent.
