Topological Mappings with Controlled $p$-Moduli

TL;DR

This paper investigates homeomorphisms characterized by controlled $p$-module integrals, establishing their properties and demonstrating their similarities to quasiconformal and bilipschitz mappings.

Contribution

It introduces a new framework for analyzing homeomorphisms via controlled $p$-moduli, connecting them to well-known classes like quasiconformal maps.

Findings

Mappings exhibit properties close to quasiconformal and bilipschitz mappings

Established bounds on features of controlled $p$-module homeomorphisms

Demonstrated the applicability of integral conditions to control mapping behavior

Abstract

We study homeomorphisms of controlled $p$-module by certain integrals. In this way, we establish various properties of mappings and show that their features are close to quasiconformal and bilipschitz mappings.