This is a preview of subscription content, log in via an institution to check access.
Literature Cited
V. V. Krivov, “On extremal quasiconformal mappings in space,” Dokl. Akad. Nauk SSSR,145, No. 3, 516–518 (1962).
V. V. Krivov, “Some properties of moduli in space” Dokl. Akad. Nauk SSSR,154, No. 3, 510–513 (1964).
V. V. Krivov, “Best extremal mappings in space,” Dokl. Akad. Nauk SSSR,155, No. 1, 38–40 (1964).
B. Fuglede, “Extremal length and functional completion,” Acta Math.,98, No. 3-4, 171–219 (1957).
B. V. Shabat, “Method of moduli in space,” Dokl. Akad. Nauk SSSR,130, No. 6, 1210–1213 (1960).
J. Väisälä, “On quasiconformal mappings in space,” Ann. Acad. Sci. Fenn. Ser. AI,298, 1–36 (1961).
S. Saks, Theory of the Integral, Dover, New York (1964).
J. Clarkson, “Uniformly convex space,” Trans. Amer. Math. Soc.,40, No. 3, 396–414 (1936).
C. Loewner, “On the conformal capacity in space,” J. Math. Mech.,8, No. 3, 411–414 (1959).
F. Gehring, “Extremal length definitions for the conformal capacity of rings in space,” Mich. Math. J.,9, No. 2, 137–150 (1962).
F. Gehring, “Rings and quasiconformal mappings in space,” Trans. Amer. Math. Soc.,103, No. 3, 353–393 (1962).
W. Ziemer, “Extremal length and conformal capacity,” Trans. Amer. Math. Soc.,126, No. 3, 460–473 (1967).
H. Federer, “Curvature measures,” Trans. Amer. Math. Soc.,93, No. 3, 418–491 (1959).
S. L. Sobolev, Some Applications of Functional Analysis in Mathematical Physics, American Math. Soc. Publ., New York (1964).
P. Caraman, Homeomorfisme cvasiconforme n-dimensionale, Bucuresti (1968).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 12, No. 5, pp. 1056–1066, September–October, 1971.
Rights and permissions
About this article
Cite this article
Krivov, V.V. The method of extremal functions in the theory of quasi-conformal mappings. Sib Math J 12, 761–768 (1971). https://doi.org/10.1007/BF00966513
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00966513