On boundary behavior of mappings with two normalized conditions |
|
| Author |
esevostyanov2009@gmail.com1,
1) Zhytomyr Ivan Franko State University
Zhytomyr, Ukraine; 2) Zhytomyr Ivan Franko State University
Zhytomyr, Ukraine; 3) Zhytomyr Ivan Franko State University
Zhytomyr, Ukraine
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| Abstract |
The paper is devoted to a study of mappings with finite distortion that have been recently
actively investigated last time. We study the boundary behavior of mappings between two fixed
domains in metric spaces, which satisfy some moduli estimates. We have proved that families
of corresponding inverse mappings with two normalized conditions and integrable majorant are
equicontinuous whenever the domain of the mappings has a weakly
at boundary
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| Keywords |
metric spaces; quasiconformal mappings; mappings with bounded and finite distortion; equicontinuity;
moduli of families of paths
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| DOI |
doi:10.15330/ms.49.2.150-157
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| Reference |
1. E. A. Sevost’yanov, S. A. Skvortsov, On convergence of mappings in metric spaces with direct and inverse
modulus conditions, Ukr. Math. Zh., 70 (2018), ¹7, 952–967. (in Russian)
2. O. Martio, V. Ryazanov, U. Srebro and E. Yakubov, Moduli in Modern Mapping Theory, Springer Monographs in Mathematics, Springer, New York etc., 2009. 3. V. Ryazanov, R. Salimov, Weakly flat spaces and boundaries in the mapping theory, Ukr. Math. Visnyk, 4 (2007), ¹2, 199–233 (in Russian); translation in Ukr. Math. Bull., 4 (2007), ¹2, 199–233. 4. E. S. Smolovaya, Boundary behavior of ring Q-homeomorphisms in metric spaces, Ukr. Mat. Zh., 62 (2010), ¹5, 682–689 (in Russian); translation in Ukr. Math. Journ., 62 (2010), ¹5, 785–793. 5. K. Kuratowski, Topology, V.2, Academic Press, New York–London, 1968. 6. E. A. Sevost’yanov, On local and boundary behavior of mappings in metric spaces, Algebra and analiz 28 (2016), ¹6, 118–146; translation Local and boundary behavior of maps in metric spaces, St. Petersburg Math. J., 28 (2017), ¹6, 807–824. 7. M. Vuorinen, On the existence of angular limits of n-dimensional quasiconformal mappings, Ark. Mat., 18 (1980), 157–180. 8. E. A. Sevost’yanov, R. R. Salimov, On inner dilatations of the mappings with unbounded characteristic, Ukr. Mat. Visnyk, 8 (2011), ¹1, 129–143 (in Russian); translation in J. Math. Sci. (N. Y.), 178 (2011), ¹1, 97–107. |
| Pages |
150-157
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| Volume |
49
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| Issue |
2
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| Year |
2018
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| Journal |
Matematychni Studii
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| Full text of paper | |
| Table of content of issue |