Quasisymmetric extension on the real line
Vellis, V. (2018). Quasisymmetric extension on the real line. Proceedings of the American Mathematical Society, 146(6), 2435-2450. https://doi.org/10.1090/proc/13346
Published in
Proceedings of the American Mathematical SocietyAuthors
Date
2018Copyright
© 2018 American Mathematical Society
We give a geometric characterization of the sets E ⊂ R for which
every quasisymmetric embedding f : E → R
n extends to a quasisymmetric
embedding f : R → RN for some N ≥ n.
Publisher
American Mathematical SocietyISSN Search the Publication Forum
0002-9939Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/27996000
Metadata
Show full item recordCollections
License
Related items
Showing items with similar title or keywords.
-
Singular quasisymmetric mappings in dimensions two and greater
Romney, Matthew (Academic Press, 2019)For all n ≥2, we construct a metric space (X, d)and a quasisymmetric mapping f:[0, 1]n→X with the property that f−1 is not absolutely continuous with respect to the Hausdorff n-measure on X. That is, there exists a Borel ... -
Quasisymmetric Koebe uniformization with weak metric doubling measures
Rajala, Kai; Rasimus, Martti (Duke University Press, 2021)We give a characterization of metric spaces quasisymmetrically equivalent to a finitely connected circle domain. This result generalizes the uniformization of Ahlfors 2-regular spaces by Merenkov and Wildrick. -
Controlled diffeomorphic extension of homeomorphisms
Koskela, Pekka; Wang, Zhuang; Xu, Haiqing (Pergamon Press, 2018)Let Ω be an internal chord-arc Jordan domain and φ:S→∂Ω be a homeomorphism. We show that φ has finite dyadic energy if and only if φ has a diffeomorphic extension h:D→Ω which has finite energy. -
Weighted estimates for diffeomorphic extensions of homeomorphisms
Xu, Haiqing (European Mathematical Society Publishing House, 2020)Let Ω⊂R2Ω⊂R2 be an internal chord-arc domain and φ:S1→∂Ωφ:S1→∂Ω be a homeomorphism. Then there is a diffeomorphic extension h:D→Ωh:D→Ω of φφ. We study the relationship between weighted integrability of the derivatives of ... -
Sobolev Extension on Lp-quasidisks
Zhu, Zheng (Springer Science and Business Media LLC, 2023)In this paper, we study the Sobolev extension property of Lp-quasidisks which are the generalizations of classical quasidisks. After that, we also find some applications of this property.