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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Bi-Lipschitz embeddings of quasiconformal trees
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by Guy C. David, Sylvester Eriksson-Bique and Vyron Vellis
Proc. Amer. Math. Soc. 151 (2023), 2031-2044
DOI: https://doi.org/10.1090/proc/16252
Published electronically: February 2, 2023

Abstract:

A quasiconformal tree is a doubling metric tree in which the diameter of each arc is bounded above by a fixed multiple of the distance between its endpoints. In this paper we show that every quasiconformal tree bi-Lipschitz embeds in some Euclidean space, with the ambient dimension and the bi-Lipschitz constant depending only on the doubling and bounded turning constants of the tree. This answers Question 1.6 of David and Vellis [Illinois J. Math. 66 (2022), pp. 189–244].
References
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Bibliographic Information
  • Guy C. David
  • Affiliation: Department of Mathematical Sciences, Ball State University, Muncie, Indiana 47306
  • MR Author ID: 1103461
  • ORCID: 0000-0002-0652-6658
  • Email: gcdavid@bsu.edu
  • Sylvester Eriksson-Bique
  • Affiliation: Research Unit of Mathematical Sciences, P.O.Box 3000, FI-90014 Oulu, Finland
  • MR Author ID: 945674
  • ORCID: 0000-0002-1919-6475
  • Email: sylvester.eriksson-bique@oulu.fi
  • Vyron Vellis
  • Affiliation: Department of Mathematics, The University of Tennessee, Knoxville, Tennessee 37966
  • MR Author ID: 1058764
  • ORCID: 0000-0003-2297-7202
  • Email: vvellis@utk.edu
  • Received by editor(s): March 3, 2022
  • Received by editor(s) in revised form: August 11, 2022, and August 31, 2022
  • Published electronically: February 2, 2023
  • Additional Notes: The first author was partially supported by NSF DMS grants 1758709 and 2054004. The second author was partially supported by the Finnish Academy grant 345005. The third author was partially supported by NSF DMS grant 1952510.
  • Communicated by: Nageswari Shanmugalingam
  • © Copyright 2023 by the authors
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 2031-2044
  • MSC (2020): Primary 30L05
  • DOI: https://doi.org/10.1090/proc/16252
  • MathSciNet review: 4556198