This is a preview of subscription content, log in via an institution to check access.
Literature Cited
J. Väisälä, Lectures on n-Dimensional Quasiconformal Mappings Springer-Verlag, Berlin (1971).
F. Caraman, n-Dimensional Quasiconformal (QCf) Mappings, Editura Academici Bucuresti, Abacus Press, Tunbridge Wells, Kent (1974).
A. K. Varisov, “The extension of spatial quasiconformal mappings,” Dokl. Akad. Nauk SSSR,234, No. 4, 740–742 (1977).
V. V. Aseev and A. K. Varisov, “A quasiconformality test for mappings of smooth surfaces,” Dokl. Akad. Nauk SSSR,234, No. 5, 1001–1003 (1977).
V. V. Aseev, “Homeomorphisms of k-dimensional spheres preserving n-dimensional spatial moduli,” Dokl. Akad. Nauk SSSR,243, No. 6, 1357–1360 (1978).
F. W. Gehring, “The Caratheodory convergence theorem for quasiconformal mappings in space,” Ann. Acad. Sci. Fenn., Ser. AI,336, No. 11, 1–21 (1963).
G. D. Suvorov, Families of Planar Topological Mappings [in Russian], Nauka, Novosibirsk (1965).
V. P. Luferenko, “An analog of Caratheodory's theorem for families of homeomorphisms of regions,” in: Metric Problems in the Theory of Functions and Mappings [in Russian], Vol. 1, Naukova Dumka, Kiev (1969), pp. 120–139.
M. A. Lavrent'ev, “Stability in Liouville's theorem,” Dokl. Akad. Nauk SSSR,95, No. 5, 925–926 (1954).
P. P. Belinskii, “Stability in Liouville's theorem in spatial conformal mappings,” in: Some Problems in Mathematics and Mechanics, for M. A. Lavrent'ev's 70th Birthday [in Russian], Nauka, Leningrad (1971), pp. 88–101.
P. P. Belinskii, “The order of closeness of spatially quasiconformal mapping to a conformal mapping,” Sib. Mat. Zh.,14, No. 3, 475–483 (1973).
Yu. G. Reshetnyak, “Stability in Liouville's theorem on conformal mappings,” in: Some Problems in Mathematics and Mechanics, for M. A. Lavrent'ev's 60th Birthday [in Russian], Izd. Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1961), pp. 219–223.
Yu. G. Reshetnyak, “Stability in Liouville's theorem on conformal mappings of regions with a nonsmooth boundary,” Sib. Mat. Zh.,17, No. 2, 361–369 (1976).
Yu. G. Reshetnyak, “Regions with the property of stability of Liouville's theorem on conformal spatial mappings,” in: Some Problems in Contemporary Function Theory. Matters of the Conference [in Russian], Izd. Inst. Mat. Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1976), pp. 185–187.
K. Kuratowski, Topology, Vol. 1, Academic Press (1966).
K. Kuratowski, Topology, Vol. 2, Academic Press (1969).
F. W. Gehring, “Quasiconformal mappings,” in: Complex Analysis and Its Applications, Lectures Int. Sem. Course, Trieste, Vol. 2, Vienna (1976), pp. 213–268.
A. V. Sychev, Spatial Quasiconformal Mappings [in Russian], Novosibirsk Univ. (1975).
P. M. Tamrazov, “The continuity of certain conformal invariants,” Ukr. Mat. Zh.,18, No. 6, 78–84 (1966).
V. A. Zorich, “Certain open problems in the theory of spatial quasiconformal mappings,” in: Metric Problems in the Theory of Functions and Mappings [in Russian], Vol. 3, Naukova Dumka, Kiev (1971), pp. 46–50.
P. Caraman, “Characterization of quasiconformality by arc families of extremal length zero,” Ann. Acad Sci. Fenn., Ser. AI,528, 1–10 (1973).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 25, No. 1, pp. 19–29, January–February, 1984.
Rights and permissions
About this article
Cite this article
Aseev, V.V. Convergence and stability of bounded modulus distortion mappings. Sib Math J 25, 15–23 (1984). https://doi.org/10.1007/BF00969504
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00969504