Abstract
It is shown that mappings in ℝn with finite distortion of area in all dimensions 1 ≤ k ≤ n − 1 satisfy certain modulus inequalities in terms of inner and outer dilatations of the mappings; in particular, generalizations of the well-known Poletskii inequality for quasiregular mappings are proved. The theory developed is applicable, for example, to the class of finitely bi-Lipschitz mappings, which is a natural generalization of the bi-Lipschitz mappings, as well as isometries and quasi-isometries in ℝn.
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