Uniformly branching trees

@article{Bonk2020UniformlyBT,
  title={Uniformly branching trees},
  author={M. Bonk and Daniel Meyer},
  journal={arXiv: Complex Variables},
  year={2020}
}
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… Expand
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