Literature Cited
I. S. Ovchinnikov, “The nonexistence of mappings of class BLn/2 of a sphere onto a domain,” Dokl. Akad. Nauk SSSR, 179, No. 1, 24–27 (1968).
B. V. Shabat, “The theory of quasiconformal mappings in space,” Dokl. Akad. Nauk SSSR,132, No. 6, 1045–1048 (1960).
J. Väisälä, “On the quasiconformal mapping of a ball,” Ann. Acad. Sci. Fenn.,304, 1–7 (1961).
V. A. Zorich, “The boundary properties of a class of mappings in space,” Dokl. Akad. Nauk SSSR,153, No. 1, 23–26 (1963).
I. S. Ovchinnikov and G. D. Suvorov, “Transformations of the Dirichlet integral in three-dimensional mappings,” Dokl. Akad. Nauk SSSR,154, No. 3, 253–256 (1964).
I. S. Ovchinnikov and G. D. Suvorov, “Transformations of the Dirichlet integral in three-dimensional mappings,” Sibirsk. Matem. Zh.,6, No. 6, 1292–1314 (1965).
F. W. Gehring and J. Väisälä, “The coefficients of quasiconformality of domains in space,” Acta Math., 114, 1–70 (1965).
A. M. Lapko and I. S. Ovchinnikov, “The nonexistence of mappings of a given class of a sphere onto a domain,” Trudy Tomsk Un-ta, 200, Vopr. Geometricheskoi Teorii Funktsii, 5, 165–172 (1968).
V. A. Zhukov and V. M. Miklyukov, “The angular boundary values of three-dimensional mappings,” Trudy Tomsk Un-ta, 200, Vopr. Geometr. Teorii Funktsii, 5, 88–95 (1968).
I. S. Ovchinnikov, “An analog of Lindeleff's theorem for three-dimensional mappings,” Metricheskie Voprosy Teorii Funktsii i Otobrazhenii, No. 1, Izd, Naukova Dumka, Kiev, 184–201 (1969).
F. W. Gehring, “Quasiconformal mappings of slit domains in 3-space,” J. Math. and Mech.,18, No. 8, 689–703 (1969).
I. S. Ovchinnikov, “Metrical properties of mappings leaving certain integral functionals bounded,” Dokl. Akad. Nauk SSSR,187, No. 1, 96–99 (1969).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 13, No. 1, pp. 142–152, January–February, 1972.
Rights and permissions
About this article
Cite this article
Ovchinnikov, I.S. A lower bound for the Dirichlet integral in the mapping of a sphere onto a domain. Sib Math J 13, 101–108 (1972). https://doi.org/10.1007/BF00967644
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00967644