On estimates of moduli of families of surfaces

TL;DR

This paper investigates a class of finite distortion space mappings with specific Luzin properties, establishing inequalities for families of surfaces measured by $k$-dimensional measures, advancing understanding in geometric function theory.

Contribution

It proves that these mappings satisfy both upper and lower inequalities for families of $k$-measure surfaces, extending existing theoretical frameworks.

Findings

Mappings satisfy upper inequalities for surface families.

Mappings satisfy lower inequalities for surface families.

Results contribute to geometric function theory.

Abstract

A class of space mappings of finite distortion with $N$ and $N^{\,-1}$ Luzin properties with respect to $k$-measured area is investigated. It is proved that, mappings mentioned above satisfy upper and lower inequalities for families of $k$-measures surfaces.