Abstract
Quasisymmetric maps f : R 1 → R 1 were introduced in 1956 in the famous paper [BA] of Beurling and Ahlfors, who proved that they are precisely the boundary maps of quasiconformal self homeomorphisms of the upper half plane fixing ∞. The present terminology was later suggested by Gehring and first published in the thesis of his student Kelingos.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Anderson, G.D., Vamanamurthy, M.K. and Vuorinen, M., Dimension-free quasiconformal distortion in n-space, Trans. Amer. Math. Soc. 297 (1986), 687–706.
Beurling, A. and Ahlfors, L., The boundary correspondence under quasiconformal mappings, Acta. Math. 96 (1956), 125–142.
Luukkainen, J. and Tukia, P., Quasisymmetric and Lipschitz approximation of embeddings, Ann. Acad. Sci. Fenn. Ser. AI Math. 6 (1981), 343–367.
Martio, O. and Sarvas, J., Injectivity theorems in plane and space, Ibid. 4 (1979), 383–401.
Tukia, P. and Väisälä, J., Quasisymmetric emJbeddings of metric spaces, Ibid. 5 (1980), 97–114.
Tukia, P. and Väisälä, J., Extension of embeddxngs close to isometries or similarities, Ibid. 9 (1984), 153–175.
Väisälä J., Quasi-symmetric embeddxngs in euclidean spaces, Trans. Amer. Math. Soc. 264 (1981), 191–204.
Väisälä J., Quasimöbius maps, J. Analyse Math. 44 (1985), 218–234.
Väisälä J., Bilipschitz and quasisymmetric extension properties, Ann. Acad. Sci. Fenn. Ser. AI Math. 11 (1986), 239–274.
Väisälä J., Porous sets and quasisymmetric maps, Trans. Amer. Math. Soc. 299 525–533.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer-Verlag New York Inc.
About this paper
Cite this paper
Väisälä, J. (1988). Quasisymmetric maps. In: Drasin, D., Kra, I., Earle, C.J., Marden, A., Gehring, F.W. (eds) Holomorphic Functions and Moduli I. Mathematical Sciences Research Institute Publications, vol 10. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9602-4_16
Download citation
DOI: https://doi.org/10.1007/978-1-4613-9602-4_16
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4613-9604-8
Online ISBN: 978-1-4613-9602-4
eBook Packages: Springer Book Archive