On removable singularities of a class of mappings (in Russian) |
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| Author |
esevostyanov2009@mail.ru, dasha.dolja@mail.ru
National Academy of Sciences of Ukraine
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| Abstract |
A paper is devoted to study of local behavior of so-called Q-mappings including quasicon-
formal mappings and mappings with bounded distortion. It is showed that, such mappings have
removable isolated singularities whenever the growth of the mappings is not more than some
function of a radius of a ball.
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| Keywords |
quasiconformal mappings; mappings with bounded and finite distortion; removable singularities;
moduli of families of curves
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| DOI |
doi:10.15330/ms.44.2.171-184
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| Reference |
1. E.A. Sevostyanov, On the local behavior of mappings with an unbounded quasiconformality coefficient,
Sib. Math. J., 53 (2012), ¹3, 520.531. (in Russian)
2. J. Vaisala, Modulus and capacity inequalities for quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A 1 Math., 509 (1972), 1-14. 3. E.A. Sevost'yanov, On removable singularities of maps with growth bounded by a function, Math. Notes., 97 (2015), ¹3, 110-121. (in Russian) 4. O. Martio, V. Ryazanov, U. Srebro, E. Yakubov, Mappings with finite length distortion, J. d'Anal. Math., 93 (2004), ¹1, 215-236. 5. O. Martio, V. Ryazanov, U. Srebro, E. Yakubov, Moduli in Modern Mapping Theory, Springer Monographs in Mathematics, Springer, New York etc., 2009. 6. C.J. Bishop, V.Ya. Gutlyanskii, O. Martio, M. Vuorinen, On conformal dilatation in space, Intern. Journ. Math. and Math. Sci., 22 (2003), 1397-1420. 7. V.Ya. Gutlyanskii, V.I. Ryazanov, U. Srebro, E. Yakubov, The Beltrami Equation: A Geometric Approach, Developments in Mathematics, V.26, Springer, New York etc., 2012. 8. A. Ignatev, V. Ryazanov, Finite mean oscillation in the mapping theory, Ukr. Math. Bull., 2 (2005), ¹3, 403-424, 443. (in Russian) 9. J. Vaisala, Lectures on n.Dimensional Quasiconformal Mappings, Lecture Notes in Math., V.229, Springer. Verlag, Berlin etc., 1971. |
| Pages |
171-184
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| Volume |
44
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| Issue |
2
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| Year |
2015
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| Journal |
Matematychni Studii
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| Full text of paper | |
| Table of content of issue |