Quasisymmetric extension on the real line
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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 $N\geq n$.References
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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
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 2435-2450
- MSC (2010): Primary 30C65; Secondary 30L05
- DOI: https://doi.org/10.1090/proc/13346
- MathSciNet review: 3778147