On convergence of homeomorphisms with inverse modulus inequality

TL;DR

This paper investigates the convergence behavior of homeomorphisms satisfying a specific inverse inequality, proving that their uniform limits are either homeomorphisms or constants in extended Euclidean space.

Contribution

It establishes a convergence result for homeomorphisms with inverse modulus inequality, clarifying the nature of their limits in Euclidean space.

Findings

Limits are either homeomorphisms or constants.

Uniform convergence preserves homeomorphism properties under inverse inequality.

Results extend understanding of homeomorphism stability in Euclidean spaces.

Abstract

We have studied homeomorphisms that satisfy the Poletsky-type inverse inequality in the domain of the Euclidean space. It is proved that the uniform limit of the family of such homeomorphisms is either a homeomorphism into the Euclidean space, or a constant in the extended Euclidean space.