Topological mappings of finite area distortion

We study the interplay of mappings of finite area distortion (FAD) with finitely bi-Lipschitz mappings, ring and lower Q-homeomorphisms, and absolutely continuous homeomorphisms of the class ACΛn,p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{AC}^{n,p}_\Lambda $$\end{document} on Riemannian manifolds. Some additional relations to the hyper Q-homeomorphisms, η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}-quasisymmetric and ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}-quasimöbius mappings are also established. As applications of the above results, we provide several extension conditions to the weakly flat and strongly accessible boundaries under FAD-homeomorphisms.