On the distortion of $n$-dimensional quasiconformal mappings
HTML articles powered by AMS MathViewer
- by Matti Vuorinen PDF
- Proc. Amer. Math. Soc. 96 (1986), 275-283 Request permission
Abstract:
A new upper bound $c(n,K)$ for the linear dilatation of a $K$-quasiconformal mapping of a domain in ${R^n}$ is proved. This upper bound substantially improves the previously known $n$-dimensional bound and it is asymptotically sharp when $n = 2$.References
- Lars V. Ahlfors, Möbius transformations in several dimensions, Ordway Professorship Lectures in Mathematics, University of Minnesota, School of Mathematics, Minneapolis, Minn., 1981. MR 725161 G. D. Anderson, M. K. Vamanamurthy and M. Vuorinen, Dimension-free, quasiconformal distortion in $n$-space (to appear).
- Alan F. Beardon, The geometry of discrete groups, Graduate Texts in Mathematics, vol. 91, Springer-Verlag, New York, 1983. MR 698777, DOI 10.1007/978-1-4612-1146-4
- F. W. Gehring, Rings and quasiconformal mappings in space, Trans. Amer. Math. Soc. 103 (1962), 353–393. MR 139735, DOI 10.1090/S0002-9947-1962-0139735-8
- F. W. Gehring, A remark on domains quasiconformally equivalent to a ball, Ann. Acad. Sci. Fenn. Ser. A I Math. 2 (1976), 147–155. MR 0486500, DOI 10.5186/aasfm.1976.0212
- F. W. Gehring, Quasiconformal mappings, Complex analysis and its applications (Lectures, Internat. Sem., Trieste, 1975) Internat. Atomic Energy Agency, Vienna, 1976, pp. 213–268. MR 0480997
- F. W. Gehring and B. G. Osgood, Uniform domains and the quasihyperbolic metric, J. Analyse Math. 36 (1979), 50–74 (1980). MR 581801, DOI 10.1007/BF02798768
- O. Lehto and K. I. Virtanen, Quasikonforme Abbildungen, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band 126, Springer-Verlag, Berlin-New York, 1965 (German). MR 0188434, DOI 10.1007/978-3-662-42594-7
- Olli Lehto, K. I. Virtanen, and Jussi Väisälä, Contributions to the distortion theory of quasiconformal mappings, Ann. Acad. Sci. Fenn. Ser. A I No. 273 (1959), 14. MR 0122990
- O. Martio, S. Rickman, and J. Väisälä, Definitions for quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A I No. 448 (1969), 40. MR 0259114
- Akira Mori, On quasi-conformality and pseudo-analyticity, Trans. Amer. Math. Soc. 84 (1957), 56–77. MR 83024, DOI 10.1090/S0002-9947-1957-0083024-5
- Ju. G. Rešetnjak, The local structure of mappings with bounded distortion, Sibirsk. Mat. Ž. 10 (1969), 1311–1333 (Russian). MR 0274755
- P. Tukia and J. Väisälä, Quasiconformal extension from dimension $n$ to $n+1$, Ann. of Math. (2) 115 (1982), no. 2, 331–348. MR 647809, DOI 10.2307/1971394 J. Väisälä, Lectures on $n$-dimensional quasiconformal mappings, Lecture Notes in Math., Vol. 229, Springer-Verlag, Berlin and New York, 1971.
- Matti Vuorinen, On the existence of angular limits of $n$-dimensional quasiconformal mappings, Ark. Mat. 18 (1980), no. 2, 157–180. MR 608334, DOI 10.1007/BF02384688
- Matti Vuorinen, Conformal invariants and quasiregular mappings, J. Analyse Math. 45 (1985), 69–115. MR 833408, DOI 10.1007/BF02792546
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 275-283
- MSC: Primary 30C60
- DOI: https://doi.org/10.1090/S0002-9939-1986-0818458-5
- MathSciNet review: 818458