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A technique for extending quasiconformal embeddings

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Part of the Lecture Notes in Mathematics book series (LNM,volume 747)

Keywords

  • Quasiconformal Mapping
  • Jordan Domain
  • Extension Technique
  • Extend QUASICONFORMAL
  • Geometric Topology

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References

  1. Ahlfors, L.: Extension of quasiconformal mappings from two to three dimensions. Proc. nat. Acad. Sci. USA 51 (1964), 768–771.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Bing, R.H.: Radial engulfing, in "Conference on the topology of manifolds". Prindle, Weber and Schmidt, Boston-London-Sydney (1968), 1–18.

    Google Scholar 

  3. Brakes, W.R.: An improved version of the non-compact weak canonical Schoenflies theorem. Trans. Amer. math. Soc. 213 (1975), 61–69.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Brown, M.: A proof of the generalized Schoenflies theorem. Bull. Amer. math. Soc. 66 (1960), 74–76.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Brown, M.: Locally flat imbeddings of topological manifolds. Ann. of math., II. Ser. 75 (1962), 331–341.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Carleson, L.: The extension problem for quasiconformal mappings, in "Contributions to analysis". Academic Press, New York and London (1974), 39–47.

    CrossRef  Google Scholar 

  7. Connell, E.H.: Approximating stable homeomorphisms by piecewise linear ones. Ann. of math., II. Ser. 78 (1963), 326–338.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Connelly, R.: A new proof of Brown's collaring theorem. Proc. Amer. math. Soc. 27 (1971), 180–182.

    MathSciNet  MATH  Google Scholar 

  9. Edwards, R.D., Kirby, R.C.: Deformations of spaces of imbeddings. Ann. of Math., II. Ser. 93 (1971), 63–88.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Gauld, D.B.: Local contractibility of spaces of homeomorphisms. Compositio math. 32 (1976), 3–11.

    MathSciNet  MATH  Google Scholar 

  11. Gauld, D.B., Vamanamurthy, M.K.: Quasiconformal extensions of mappings in n-space. Ann. Acad. Sci. Fenn., Ser. A I 3 (1977), 229–246.

    MathSciNet  MATH  Google Scholar 

  12. Gauld, D.B., Vamanamurthy, M.K.: A special case of Schönflies theorem for quasiconformal mappings in n-space. Ann. Acad. Sci. Fenn., Ser. A I 3 (1977), 311–316.

    MathSciNet  MATH  Google Scholar 

  13. Gehring, F.W.: Extension theorems for quasiconformal mappings in n-space. J. Analyse math. 19 (1967), 149–169.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Mazur, B.C.: On embeddings of spheres. Acta math. 105 (1961), 1–17.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. Moise, E.E.: Geometric topology in dimensions 2 and 3. Springer-Verlag, New York-Berlin-Heidelberg (1977).

    CrossRef  MATH  Google Scholar 

  16. Morse, M.: A reduction of the Schoenflies extension problem. Bull. Amer. math. Soc. 66 (1960), 113–115.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. Näkki, R.: Boundary behaviour of quasiconformal mappings in n-space. Ann. Acad. Sci. Fenn., Ser. A I 484 (1970), 1–50.

    MATH  Google Scholar 

  18. Rushing, T.B.: Topological embeddings. Academic Press, New York and London (1973).

    MATH  Google Scholar 

  19. Siebenmann, L.C.: Deformations of homeomorphisms on stratified sets. Commentarii math. Helvet. 47 (1972), 123–163.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. Väisälä, J.: Lectures on n-dimensional quasiconformal mappings. Lecture Notes in Mathematics 229, Springer-Verlag, Berlin-Heidelberg-New York (1971).

    MATH  Google Scholar 

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© 1979 Springer-Verlag

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Gauld, D.B. (1979). A technique for extending quasiconformal embeddings. In: Laine, I., Lehto, O., Sorvali, T. (eds) Complex Analysis Joensuu 1978. Lecture Notes in Mathematics, vol 747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0063966

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  • DOI: https://doi.org/10.1007/BFb0063966

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09553-8

  • Online ISBN: 978-3-540-34859-7

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