References
L. V. Ahlfors, Lectures on Quasiconformal Mappings [Russian translation], Mir, Moscow (1969).
P. Tukia and J. Väisälä, “Lipschitz and quasiconformal approximation and extension,” Ann. Acad. Sci. Fenn. Ser. AI Math.,6, No. 2, 303–342 (1981).
T. G. Latfullin, “On smoothing quasiconformal involutions,” submitted to VINITI on March 7, 1985, No. 1730-85.
Yu. G. Reshetnyak, Space Mappings with Bounded Distortion [in Russian], Nauka, Novosibirsk (1982).
P. Caraman, “On the equivalence of the definitions of then-dimensional quasiconformal homeomorphisms (QCFH),” Rev. Roumaine Math. Pures Appl.,12, No. 7, 889–943 (1967).
F. W. Gehring and B. G. Osgood, “Uniform domains and the quasihyperbolic metric,” J. Anal. Math.,36, 50–74 (1979).
T. G. Latfullin, “A quasihyperbolicity criterion for mappings,” Sibirsk. Mat. Zh.,37, No. 3, 611–615 (1996).
P. A. Smith, “Fixed points for periodic transformations” in: Supplement B to the book: S. Lefschetz, Algebraic Topology [Russian translation], Izdat., Inostr. Lit., Moscow (1949).
J. Väisälä, Lectures onn-Dimensional Quasiconformal Mappings, Springer, Berlin, Heidelberg, and New York (1971).
M. de Guzmán, Differentiation of Integrals in ℝn [Russian translation], Mir, Moscow (1978).
J. Väisälä, “Quasi-symmetric embeddings in Euclidean spaces,” Trans. Amer. Math. Soc.,264, 191–204 (1981).
J. Väisälä, “Uniform domains,” Tôhoku Math. J. (2),40, No. 1, 101–118 (1988).
Additional information
Dedicated to my teacher Yuriî Grigor′evich Reshetnyak.
Tyumen′. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 40, No. 4, pp. 918–930, July–August, 1999.
Tyumen′. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 40, No. 4, pp. 918–930, July–August, 1999.
Rights and permissions
About this article
Cite this article
Latfullin, T.G. A generalization of the ahlfors theorem on quasi-isometric reflection. Sib Math J 40, 775–786 (1999). https://doi.org/10.1007/BF02675676
Issue Date:
DOI: https://doi.org/10.1007/BF02675676