References
L. V. Ahlfors, Extension of quasiconformal mappings from two to three dimensions,Proc. Nat. Acad. Sci. 51 (1964) pp. 768–771.
M. Brown, A proof of the generalized Schoenflies theorem,Bull. Amer. Math. Soc. 66 (1960) pp. 74–76.
M. Brown, Locally flat imbeddings of topological manifolds,Ann. Math. 75 (1962) pp. 331–341.
Han-lin Chen, Quasiconformal mappings inn-dimensional space,Acta Math. Sinica 14 (1964) pp. 93–102 (Chinese); translated inChinese Math. Acta 5 (1964) pp. 101–111.
F. W. Gehring, Rings and quasiconformal mappings in space,Trans. Amer. Math. Soc. 103 (1962) pp. 353–393.
F. W. Gehring, Extension of quasiconformal mappings in three space,J. d'Analyse Math. 14 (1965) pp. 171–182.
F. W. Gehring and J. Väisälä, The coefficients of quasiconformality of domains in space,Acta Math. 114 (1965) pp. 1–70.
J. Hersch, Contribution à la théorie des fonctions pseudo-analytiques,Comm. Math. Helv. 30 (1956) pp. 1–19.
W. Huebsch and M. Morse, An explicit solution of the Schoenflies extension problem,J. Math. Soc. Japan12 (1960) pp. 271–289.
O. Lehto and K. I. Virtanen, Quasikonforme Abbildungen, Springer-Verlag, Berlin-Heidelberg-New York 1965.
B. Mazur, On embeddings of spheres,Bull. Amer. Math. Soc. 65 (1959) pp. 59–65.
M. Morse, A reduction of the Schoenflies extension problem,Bull. Amer. Math. Soc. 66 (1960) pp. 113–115.
J. Väisälä, On quasiconformal mappings in space,Ann. Acad. Sci. Fenn. 298 (1961) pp. 1–36.
J. Väisälä, Two new characterizations for quasiconformality,Ann Acad. Sci. Fenn. 362 (1965) pp. 1–12.
R. L. Wilder, Topology of manifolds, Amer. Math. Soc. Colloquium Publications Vol.32, New York 1949.
Author information
Authors and Affiliations
Additional information
This research was supported in part by the National Science Foundation, Contract GP-4153.
Rights and permissions
About this article
Cite this article
Gehring, F.W. Extension theorems for quasiconformal mappings inn-space. J. Anal. Math. 19, 149–169 (1967). https://doi.org/10.1007/BF02788713
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02788713