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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Uniformly branching trees
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by Mario Bonk and Daniel Meyer PDF
Trans. Amer. Math. Soc. 375 (2022), 3841-3897 Request permission


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.
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Additional Information
  • Mario Bonk
  • Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095
  • MR Author ID: 39235
  • Email:
  • 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:
  • 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:
  • MathSciNet review: 4419049