Nagoya Mathematical Journal

Thick sets and quasisymmetric maps

Matti Vuorinen, Jussi Väisälä, and Hans Wallin

Full-text: Open access

Article information

Source
Nagoya Math. J., Volume 135 (1994), 121-148.

Dates
First available in Project Euclid: 14 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1118780004

Mathematical Reviews number (MathSciNet)
MR1295820

Zentralblatt MATH identifier
0803.30016

Subjects
Primary: 30C65: Quasiconformal mappings in $R^n$ , other generalizations

Citation

Väisälä, Jussi; Vuorinen, Matti; Wallin, Hans. Thick sets and quasisymmetric maps. Nagoya Math. J. 135 (1994), 121--148. https://projecteuclid.org/euclid.nmj/1118780004


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References

  • [AG] S. Agard andF.W. Gehring, Angles andquasiconformal mappings,Proc. London Math. Soc,14A (1965),1-21.
  • [AW] G.D.Anderson, M.K. Vamanamurthy and M.Vuorinen, Inequalities for quasi- conformal maps in space, Pacific Math. J.,160(1993), 1-18.
  • [Be] M.Berger, Geometry I,Springer-Verlag,1987.
  • [Bl] L. M.Blumenthal, Theory and applications of distance geometry, Oxford atthe Clarendon Press, 1953.
  • [Ha] H.Hadwiger, Vorlesungen ber Inhalt, Oberflache und Isoperimetrie, Springer-
  • [JW] A. Jonsson and H. Wallin, Function spaces on subsets of Rn, Harwood Acad. PubL, 1984.
  • [MVJP.Matti] a and M. Vuorinen, Linear approximation property, Minkowski dimen- sion and quasiconformal spheres, J. London Math. Soc, (2) 42 (1990), 249–269.
  • [NV] R. Nakki and J. Vaisala, John disks, Exposition. Math,. 9 (1991), 3-43.
  • [Pa] J. Partanen, Invariance theorems for the bilipschitz and quasisymmetric exten- sion properties, Ann. Acad. Sci. Fenn. Ser. A I Math. Diss. 80 (1990), 1-40.
  • [Ri] S. Rickman, Characterization of quasiconformal arcs, Ann. Acad. Sci. Fenn. Ser. A I Math., 395 (1966), 1-30.
  • [Ro] S. Rohde, On conformal welding and quasicircles, Michigan Math. J., 38 (1991), 111-116.
  • [So] D. M. Y. Sommerville, An introduction to the geometry of n dimensions, Dover Publications, 1958.
  • [TVi] P. Tukia and J. Vaisala, Quasisymmetric embeddings of metric spaces, Ann. Acad. Sci. Fenn. Ser. A I Math., 5 (1980), 97-114.
  • [TV2] P. Tukia and J. Vaisala, Extension of embeddings close to isometries or similarities, Ann. Acad. Sci. Fenn. Ser. A I Math., 9 (1984), 153-175.
  • [Vai] J. Vaisala, Lectures on w-dimensional quasiconformal mappings, Lecture Notes in Mathematics, 229, Springer-Verlag, 1971.
  • [Va2] J. Vaisala, Quasimbius maps, J. Analyse Math., 44, (1984/85), 218-234.
  • [Va3] J. Vaisala, Bilipschitz and quasisymmetric extension properties, Ann. Acad. Sci. Fenn. Ser. A I Math., 11 (1986), 239-274.
  • [Va4] J. Vaisala, Quasiconformal maps of cylindrical domains, Acta Math., 162 (1989), 201-225.
  • [VV] M. K. Vamanamurthy and M. Vuorinen, Functional inequalities, Jacobi products, and quasiconformal maps, Illinois J. Math., 38 (1994), 394-419.
  • [Vu] M. Vuorinen, Quadruples and spatial quasiconformal mappings, Math. Z., 205 (1990), 617-628.
  • [WW]. Approx. Theory 69 (1992), 231-249. J. Vaisala and M. Vuorinen Mathematiikan laitos Helsingin yliopisto Hallituskatu 15 FIN-00100 Helsinki Finland Matematiska institutionen Umea universitet S-90187 Umea Sweden