On the theory of mappings with finite area distortion
The authors study the class FAD that consists of mappings in \(\mathbb{R}^n\), \(n\geq 2\), with finite area distortion. This family includes the class FLD (maps of finite length distortion) studied earlier by \textit{O. Martio} et al. [J. Anal. Math. 93, 215--236 (2004; Zbl 1084.30021)] and is the widest to which the classical modulus ineqalities of the quasiregular theory can be extended. The authors give the Fubini type theorems for moduli, estimate moduli from above (the Poleckij type inequality) and from below. Then they apply their results to finitely bi-Lipschitz mappings. They show, for example, that every bi-Lipschitz homeomorphism is in FAD.
scientific article; zbMATH DE number 5320478