Geodesic
Equicontinuity of Families of Mappings with One Normalization Condition
Matematičeskie zametki, Tome 109 (2021) no. 4, pp. 597-607 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the behavior of a certain class of mappings of a domain in Euclidean space. We prove that this class is equicontinuous both at the interior and boundary points, of the domain provided that it consists of mappings that satisfy a common normalization condition and whose quasiconformality characteristic has only tempered growth in a neighborhood of each point in the closure of the domain.
Mots-clés : quasiconformal analysis
Keywords: mapping with bounded and finite distortion, local and boundary behavior of a mapping. 
@article{MZM_2021_109_4_a10,
     author = {E. A. Sevost'yanov and S. Sergei},
     title = {Equicontinuity of {Families} of {Mappings} with {One} {Normalization} {Condition}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {597--607},
     year = {2021},
     volume = {109},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_4_a10/}
}
TY  - JOUR
AU  - E. A. Sevost'yanov
AU  - S. Sergei
TI  - Equicontinuity of Families of Mappings with One Normalization Condition
JO  - Matematičeskie zametki
PY  - 2021
SP  - 597
EP  - 607
VL  - 109
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_2021_109_4_a10/
LA  - ru
ID  - MZM_2021_109_4_a10
ER  - 
%0 Journal Article
%A E. A. Sevost'yanov
%A S. Sergei
%T Equicontinuity of Families of Mappings with One Normalization Condition
%J Matematičeskie zametki
%D 2021
%P 597-607
%V 109
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_2021_109_4_a10/
%G ru
%F MZM_2021_109_4_a10
E. A. Sevost'yanov; S. Sergei. Equicontinuity of Families of Mappings with One Normalization Condition. Matematičeskie zametki, Tome 109 (2021) no. 4, pp. 597-607. http://geodesic.mathdoc.fr/item/MZM_2021_109_4_a10/

[1] O. Martio, V. Ryazanov, U. Srebro, E. Yakubov, Moduli in Modern Mapping Theory, Springer, New York, 2009 | MR | Zbl

[2] V. Gutlyanskii, V. Ryazanov, E. Yakubov, “The Beltrami equations and prime ends”, J. Math. Sci. (N.Y.), 210:1 (2015), 22–51 | MR | Zbl

[3] E. A. Sevostyanov, S. A. Skvortsov, “O ravnostepennoi nepreryvnosti semeistv otobrazhenii v sluchae peremennykh oblastei”, Ukr. matem. zhurn., 71:7 (2019), 938–951 | MR | Zbl

[4] J. Väisälä, Lectures on $n$-Dimensional Quasiconformal Mappings, Lecture Notes in Math., 229, Springer-Verlag, Berlin, 1971 | DOI | Zbl

[5] R. Näkki, B. Palka, “Uniform equicontinuity of quasiconformal mappings”, Proc. Amer. Math. Soc., 37:2 (1973), 427–433 | DOI | MR | Zbl

[6] D. P. Ilyutko, E. A. Sevostyanov, “O prostykh kontsakh na rimanovykh mnogoobraziyakh”, Ukr. matem. vestnik, 15:3 (2018), 358–392 | MR

[7] D. A. Kovtonyuk, V. I. Ryazanov, “Prostye kontsy i klassy Orlicha–Soboleva”, Algebra i analiz, 27:5 (2015), 81–116 | MR

[8] E. A. Sevostyanov, “O granichnom prodolzhenii i ravnostepennoi nepreryvnosti semeistv otobrazhenii v terminakh prostykh kontsov”, Algebra i analiz, 30:6 (2018), 97–146

[9] R. Näkki, “Prime ends and quasiconformal mappings”, J. Anal. Math., 35 (1979), 13–40 | DOI | MR | Zbl

[10] E. A. Sevostyanov, Issledovanie prostranstvennykh otobrazhenii geometricheskim metodom, Naukova dumka, Kiev, 2014

[11] E. A. Sevostyanov, “O ravnostepennoi nepreryvnosti gomeomorfizmov s neogranichennoi kharakteristikoi”, Matem. tr., 15:1 (2012), 178–204 | MR | Zbl

[12] O. Lehto, K. Virtanen, Quasiconformal Mappings in the Plane, Springer, New York, 1973 | MR | Zbl

[13] R. Näkki, “Extension of Loewner's capacity theorem”, Trans. Amer. Math. Soc., 180 (1973), 229–236 | MR | Zbl