Article PDF
Avoid common mistakes on your manuscript.
References
L. Ahlfors and A. Beurling,Conformal invariants and function-theoretic null-sets, Acta Math.83 (1950), 101–129.
V. Aseev and A. Syčev,On the removable sets of spatially quasiconformal mappings (Russian), Sibirsk. Mat. Ž.15 (1974), 1213–1227.
A. Beurling and L. Ahlfors,The boundary correspondence under quasiconformal mappings, Acta Math.96 (1956), 125–142.
F. W. Gehring,Symmetrization of rings in space, Trans. Am. Math. Soc.101 (1961), 499–519.
F. W. Gehring,Extension of quasiconformal mappings in three space, J. Analyse Math.14 (1965). 171–182.
F. W. Gehring,Univalent functions and the Schwarzian derivative, Comment. Math. Helv.52 (1977), 561–572.
F. W. Gehring,Injectivity of local quasi-isometries, Comment. Math. Helv.57 (1982), 202–220.
F. W. Gehring,Characteristic properties of quasidisks, Séminaire de Mathématiques Supérieures, Université de Montréal, Les Presses de l'Université de Montréal, 1982.
F. W. Gehring and O. Martio,Lipschitz classes and quasiconformal mappings, Ann. Acad. Sci. Fenn. A I Math.10 (1985), 203–219.
F. W. Gehring and B. P. Palka,Quasiconformally homogeneous domains, J. Analyse Math.36 (1979), 50–74.
F. W. Gehring and B. P. Palka,Quasiconformally homogeneous domains, J. Analyse Math.30 (1976), 172–199.
V. M. Gol'dstein and S. K. Vodop'janov,Prolongement des fonctions de classe L p′ et applications quasiconformes, C. R. Acad. Sci. Paris290 (1980), 453–456.
H. Grötzsch,Eine Bemerkung zum Koebeschen Kreisnormierungsprinzip, Berichte über die Verhandlungen der Sächsischen Akademie der Wissenschaften zu Leibzig87 (1936), 319–324.
J. Hesse,A p-extremal length and p-capacity equality, Ark. Mat.13 (1975), 131–144.
P. W. Jones,Quasiconformal mappings and extendability of functions in Sobolev spaces, Acta Math.147 (1981), 71–88.
M. Jurchescu,Modulus of a boundary component, Pacific J. Math.8 (1958), 791–809.
O. Martio,Definitions for uniform domains, Ann. Acad. Sci. Fenn. A I Math.5 (1980), 197–205.
O. Martio and J. Sarvas,Injectivity theorems in plane and space, Ann. Acad. Sci. Fenn. A I Math.4 (1978/79), 383–401.
M. H. A. Newman,Elements of the topology of plane sets of points, Cambridge Univ. Press, Cambridge, 1954.
B. G. Osgood,Univalence criteria in multiply-connected domains, Trans. Am. Math. Soc.260 (1980), 459–473.
J. Väisälä,On the null-sets for extremal distances, Ann. Acad. Sci. Fenn. A I Math.322 (1962), 1–12.
J. Väisälä,Lectures on n-dimensional quasiconformal mappings, Lecture Notes in Mathematics229, Springer-Verlag, Berlin, 1971.
M. F. Walker,Linearly locally connected sets and quasiconformal mappings, Ann. Acad. Sci. Fenn. A I Math., to appear.
R. L. Wilder,Topology of manifolds, A. M. S. Colloquium Publication No. 32, New York, 1949.
Author information
Authors and Affiliations
Additional information
This research was supported in part by grants from the U.S. National Science Foundation and from the Humboldt Foundation of West Germany.
Rights and permissions
About this article
Cite this article
Gehring, F.W., Martio, O. Quasiextremal distance domains and extension of quasiconformal mappings. J. Anal. Math. 45, 181–206 (1985). https://doi.org/10.1007/BF02792549
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02792549