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Quasisymmetric extension on the real line


Author: Vyron Vellis
Journal: Proc. Amer. Math. Soc. 146 (2018), 2435-2450
MSC (2010): Primary 30C65; Secondary 30L05
DOI: https://doi.org/10.1090/proc/13346
Published electronically: March 12, 2018
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Abstract: We give a geometric characterization of the sets $ E\subset \mathbb{R}$ for which every quasisymmetric embedding $ f: E \to \mathbb{R}^n$ extends to a quasisymmetric embedding $ f:\mathbb{R}\to \mathbb{R}^N$ for some $ N\geq n$.


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Additional Information

Vyron Vellis
Affiliation: Department of Mathematics and Statistics, P.O. Box 35 (MaD), FI-40014 University of Jyväskylä, Jyväskylä, Finland
Address at time of publication: Department of Mathematics, University of Connecticut, 341 Mansfield Rd, Storrs, CT 06269, USA
Email: vyron.vellis@uconn.edu

DOI: https://doi.org/10.1090/proc/13346
Keywords: Quasisymmetric extension, relatively connected sets
Received by editor(s): October 19, 2015
Received by editor(s) in revised form: June 2, 2016, June 12, 2016, and June 24, 2016
Published electronically: March 12, 2018
Additional Notes: The author was supported by the Academy of Finland project 257482.
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2018 American Mathematical Society

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