# 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

#### 4 Citations

#### References

SHOWING 1-10 OF 28 REFERENCES

Quasisymmetric conjugacy between quadratic dynamics and iterated function systems

- Mathematics
- Ergodic Theory and Dynamical Systems
- 2009

Weighted partition of a compact metrizable space, its hyperbolicity and Ahlfors regular conformal dimension

- Mathematics
- 2018