On removable singularities of mappings in uniform spaces 

Author 
esevostyanov2009@gmail.com^{1}, serezha.skv@gmail.com^{2}, ilkevych@list.ru^{2}
1) Zhytomyr Ivan Franko State University
Zhytomyr, Ukraine
Institute of Applied Mathematics and Mechanics
of NAS of Ukraine, Slovyansk, Ukraine; 2, 3) Zhytomyr Ivan Franko State University
Zhytomyr, Ukraine

Abstract 
The paper is devoted to the study of mappings of two metric spaces that distort the modulus
of families of paths by analogy with the Poletskii
inequality.We deal with the situation when the
mapping acts in a space that admits weak sphericalization, while the corresponding extended
metric space is uniform. For such mappings, the possibility of continuous extension to an
isolated boundary point is proved and, as a consequence, an analogue of the SokhotskiCasoratiWeierstrass theorem is obtained.

Keywords 
metric spaces; quasiconformal mappings; mappings with bounded and finite distortion; singularities;
moduli of families of paths

DOI 
doi:10.30970/ms.52.1.2431

Reference 
1. E. Afanaseva, A. Golberg, R. Salimov, Finite mean oscillation in upper ular metric spaces, Lobachevskii
J. Math., 38 (2017), ¹2, 206212.
2. E. Afanaseva, R. Salimov, Boundary behavior of mappings in $\lambda(\varepsilon)$regular metric spaces, J. Math. Sci., 211 (2015), ¹5, 617623. 3. A. Ignatev, V. Ryazanov, Finite mean oscillation in the mapping theory, Ukr. Mat. Visn., 2 (2005), ¹3, 395.417 (in Russian); translation Finite mean oscillation in the mapping theory, Ukr. Math. Bull., 2 (2005), ¹3, 403424. 4. O. Martio, V. Ryazanov, U. Srebro, E. Yakubov, Moduli in Modern Mapping Theory, Springer Monographs in Mathematics, Springer, New York etc., 2009. 5. R. Nakki and B. Palka, Uniform equicontinuity of quasiconformal mappings, Proc. Amer. Math. Soc., 37 (1973), ¹2, 427433. 6. S. Rickman, Quasiregular mappings, Berlin etc., SpringerVerlag, 1993. 7. V. Ryazanov, R. Salimov,Weakly flat spaces and boundaries in the mapping theory, Ukr. Math. Visnyk, 4 (2007), ¹2, 199233 (in Russian); translation Weakly flat spaces and boundaries in the mapping theory, Ukr. Math. Bull., 4 (2007), ¹2, 199233. 8. E.A. Sevostyanov, A.A. Markysh, On SokhotskiCasoratiWeierstrass theorem on metric spaces, Complex Variables and Elliptic Equations, published online https://www.tandfonline.com/doi/full/ 10.1080/17476933.2018.1557155. 9. J. Vaisala, Lectures on ndimensional quasiconformal mappings, Lecture Notes in Math., V.229, Springer.Verlag, Berlin etc., 1971. 10. B. Fuglede, Extremal length and functional completion, Acta Math., 98 (1957), 171219. 11. J. Heinonen, Lectures on Analysis on metric spaces, Springer Science+Business Media, New York, 2001. 12. K. Kuratowski, Topology, V.2, Academic Press, New YorkLondon, 1968. 
Pages 
2431

Volume 
52

Issue 
1

Year 
2019

Journal 
Matematychni Studii

Full text of paper  
Table of content of issue 