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 AC(Lambda)(n,p) on Riemannian manifolds. Some additional relations to the hyper Q-homeomorphisms, eta-quasisymmetric and omega-quasimobius 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.