Uniformly branching trees
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- by Mario Bonk and Daniel Meyer PDF
- Trans. Amer. Math. Soc. 375 (2022), 3841-3897 Request permission
Abstract:
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.References
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Additional Information
- Mario Bonk
- Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095
- MR Author ID: 39235
- Email: mbonk@math.ucla.edu
- Daniel Meyer
- Affiliation: Department of Mathematical Sciences, University of Liverpool, Mathematical Sciences Building, Liverpool L69 7ZL, United Kingdom
- MR Author ID: 700302
- ORCID: 0000-0003-1881-8137
- Email: dmeyermail@gmail.com
- Received by editor(s): June 2, 2020
- Received by editor(s) in revised form: January 21, 2021
- Published electronically: March 4, 2022
- Additional Notes: The first author was partially supported by NSF grant DMS-1808856
- © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 375 (2022), 3841-3897
- MSC (2020): Primary 30L10
- DOI: https://doi.org/10.1090/tran/8404
- MathSciNet review: 4419049