Published Paper

Inserted: 17 jan 2025
Last Updated: 17 jan 2025

Journal: Russian Mathematics
Volume: 68
Number: 3
Pages: 70-75
Year: 2024
Doi: 10.3103/S1066369X24700208
Links: Publisher page, ResearchGate page

Abstract:

In this paper we study the locally uniform convergence of homeomorphisms with bounded $(1,\sigma)$-weighted $(q,p)$-distortion to a limit homeomorphism. Under some additional conditions we prove that the limit homeomorphism is a mapping with bounded $(1,\sigma)$-weighted $(q,p)$-distortion. Moreover, we obtain the property of lower semicontinuity of distortion characteristics of homeomorphisms.

Keywords: Lower Semicontinuity, Carnot group, homeomorphism with bounded $(1,\sigma)$-weighted $(q,p)$-distortion