References
Yu. G. Reshetnyak, Space Mappings with Bounded Distortion [in Russian], Nauka, Novosibirsk (1982).
A. V. Chernavskiĩ, “Finite-to-one open mappings on manifolds,” Mat. Sb.,65, No. 3, 357–369 (1964).
J. Väisälä, “Discrete open mappings on manifolds,” Ann. Acad. Sci. Fenn. Ser. AI Math.,392, 1–10 (1966).
O. Martio, S. Rickman, and J. Väisälä, “Topological and metric properties of quasiregular mappings,” Ann. Acad. Sci. Fenn. Ser. AI Math.,488, 1–31 (1971).
V. M. Gol'dshtein, “On the behavior of mappings with bounded distortion when the distortion coefficient is close to 1,” Sibirsk. Mat. Zh.,12, No. 6, 1250–1258 (1971).
O. Martio, “A capacity inequality for quasiregular mappings,” Ann. Acad. Sci. Fenn. Ser. AI Math.,474, 1–18 (1970).
E. A. Poletskiĩ, “The method of modules for nonholomorphic quasiconformal mappings,” Mat. Sb.,92, No. 2, 242–256 (1973).
S. Rickman, “Sets with large local index of quasiregular mappings in dimension three,” Ann. Acad. Sci. Fenn. Ser. AI Math.,10, 493–498 (1985).
J. Sarvas, “Coefficient of the injectivity for quasiregular mappings,” Duke Math. J.,43, 147–158 (1976).
O. Martio and J. Sarvas, “Injectivity theorems in plane and space,” Ann. Acad. Sci. Fenn. Ser. AI Math.,4, No. 2, 383–401 (1979).
V. I. Semënov, “Stability estimates for quasiconformal space mappings over a starlike domain,” Sibirsk. Mat. Zh.,28, No. 6, 102–118 (1987).
V. I. Semënov, “Stability estimates, distortion theorems, and topological properties of mappings with bounded distortion,” Mat. Zametki,51, No. 5, 109–113 (1992).
J. Väisälä, Lectures on n-Dimensional Quasiconformal Mappings, Springer, Berlin (1979) (Lecture Notes in Math.,229).
V. M. Gol'dshtein and Yu. G. Reshetnyak, Introduction to the Theory of Functions with Generalized Derivatives and the Quasiconformal Mappings [in Russian], Nauka, Moscow (1983).
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Translated from Sibirskiĩ Matematicheskiĩ, Vol. 36, No. 2, pp. 404–408, March–April, 1995.
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Semënov, V.I. Local homeomorphy of some mappings with bounded distortion and quasiconformality coefficient less than two. Sib Math J 36, 354–358 (1995). https://doi.org/10.1007/BF02110158
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DOI: https://doi.org/10.1007/BF02110158