On direct and inverse Poletsky inequalities with a tangential dilatation-Reference-Cited by-同舟云学术

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On direct and inverse Poletsky inequalities with a tangential dilatation

Published:2024-02-01 Issue:1 Volume:74 Page:91-114
ISSN:0139-9918
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Sevost’yanov Evgeny¹²,Targonskii Valery¹

Affiliation:

1. Zhytomyr Ivan Franko State University Velyka Berdychivs’ka Str. 40 Zhytomyr Ukraine

2. Institute of Applied Mathematics and Mechanics of NAS of Ukraine , Henerala Batyuka Str. 19 Slov’yans’k Ukraine

Abstract

Abstract This article is devoted to the study of mappings defined in the plane domain. Under certain conditions, the upper estimate of the distortion of the modulus of families of paths is obtained. Similarly, the upper estimate of the modulus of the families of paths in the pre-image under the mapping is also obtained.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/ms-2024-0007/pdf

Reference36 articles.

1. Ahlfors, L.: Lectures on Quasiconformal Mappings, Van Nostrand, New York, 1966.

2. Bojarski, B.—Iwaniec, T.: Analytical foundations of the theory of quasiconformal mappings in ℝn, Ann. Acad. Sci. Fenn. Ser. A. I. Math. 8 (1983), 257–324.

3. Federer, H.: Geometric Measure Theory, Springer, Berlin, 1969.

4. Gehring, F. W.: Rings and quasiconformal mappings in space, Trans. Amer. Math. Soc. 103 (1962), 353–393.

5. Golberg, A.—Salimov, R.—Sevost’yanov, E.: Normal families of discrete open mappings with controlled p-module, Contemp. Math. 667 (2016), 83–103.

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