Mathematische Annalen

, Volume 269, Issue 4, pp 561–572 | Cite as

Bilipschitz extensions of maps having quasiconformal extensions

  • Pekka Tukia
  • Jussi Väisälä


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  1. [A]
    Ahlfors, L.V.: Lectures on quasiconformal mappings. Van Nostrand Mathematical Studies 10, 1966Google Scholar
  2. [F]
    Federer, H.: Geometric measure theory. Berlin, Heidelberg, New York: Springer 1969Google Scholar
  3. [G1]
    Gehring, F.W.: Extension theorems for quasiconformal mappings inn-space. Proceedings ICM 1966, 313–318, Moscow, 1968Google Scholar
  4. [G2]
    Gehring, F.W.: Injectivity of local quasi-isometries. Comment. Math. Helv.57, 202–220 (1982)Google Scholar
  5. [GO]
    Gehring, F.W., Osgood, B.G.: Uniform domains and the quasihyperbolic metric. J. Anal. Math.36, 50–74 (1979)Google Scholar
  6. [L]
    Latfullin, T.G.: On the extension of quasi-isometric mappings (Russian). Sibirsk. Mat. Ž.24/4, 212–216 (1983)Google Scholar
  7. [LV]
    Lehto, O., Virtanen, K.I.: Quasiconformal mappings in the plane. Berlin, Heidelberg, New York: Springer 1973Google Scholar
  8. [R]
    Rushing, T.B.: Topological embeddings. London, New York: Academic Press 1973Google Scholar
  9. [T]
    Tukia, P.: The planar Schönflies theorem for Lipschitz maps. Ann. Acad. Sci. Fenn. Ser. AI5, 49–72 (1980)Google Scholar
  10. [TV1]
    Tukia, P., Väisälä, J.: Quasisymmetric embeddings of metric spaces. Ann. Acad. Sci. Fenn. Ser. AI5, 97–114 (1980)Google Scholar
  11. [TV2]
    Tukia, P., Väisälä, J.: Quasiconformal extension from dimensionn ton+1. Ann. Math.115, 331–348 (1982)Google Scholar
  12. [TV3]
    Tukia, P., Väisälä, J.: Lipschitz and quasiconformal approximation and extension. Ann. Acad. Sci. Fenn. Ser. AI6, 303–342 (1981)Google Scholar
  13. [TV4]
    Tukia, P., Väisälä, J.: Extension of embeddings close to isometries or similarities. Ann. Acad. Sci. Fenn. Ser. AI9, 153–175 (1984)Google Scholar
  14. [V1]
    Väisälä, J.: Lectures onn-dimensional quasiconformal mappings. Lecture Notes in Mathematics, Vol. 229. Berlin, Heidelberg, New York: Springer 1971Google Scholar
  15. [V2]
    Väisälä, J.: Piecewise quasiconformal maps are quasiconformal. Ann. Acad. Sci. Fenn. Ser. AI1, 3–6 (1975)Google Scholar
  16. [V3]
    Väisälä, J.: Quasi-symmetric embeddings in euclidean spaces. Trans. Am. Math. Soc.264, 191–204 (1981)Google Scholar
  17. [V4]
    Väisälä, J.: Quasimöbius maps (to appear)Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Pekka Tukia
    • 1
  • Jussi Väisälä
    • 1
  1. 1.Department of MathematicsUniversity of HelsinkiHelsinki 10Finland

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