On direct and inverse Poletsky inequality with a tangential dilatation on the plane

TL;DR

This paper investigates the behavior of certain plane mappings, providing upper estimates for the distortion of path family moduli and their pre-images under specific conditions.

Contribution

It introduces new upper bounds for the modulus distortion of path families and their pre-images in plane mappings with tangential dilatation.

Findings

Derived upper estimates for modulus distortion

Established conditions for mappings with tangential dilatation

Analyzed the behavior of path families under these mappings

Abstract

This article is devoted to the study of mappings defined in the region on the plane. 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.