# On Poletsky type inequality for mappings of Riemannian surfaces

## TL;DR

This paper establishes upper bounds on how mappings of Sobolev class distort path families on Riemannian surfaces, leading to insights into their local and boundary behavior.

## Contribution

It provides new upper estimates for the modulus distortion of Sobolev mappings on Riemannian surfaces, advancing understanding of their geometric properties.

## Key findings

- Derived upper bounds for modulus distortion under Sobolev mappings
- Results on local behavior of mappings with integrable dilatation
- Boundary behavior theorems for these mappings

## Abstract

In this paper, we obtain upper estimates for the distortion of the modulus of families of paths under mappings of the Sobolev class, whose dilatation is locally integrable. As a consequence, theorems on the local and boundary behavior of the indicated mappings are obtained.