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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机译：结果表明，在所有维度1≤k≤n -1中，具有有限面积畸变的ℝ n 中的映射在映射的内部和外部扩展方面都满足一定的模量不等式。特别地，证明了准正则映射的众所周知的Poletskii不等式的推广。所发展的理论适用于例如有限双利普希兹映射的一类，它是bi-Lipschitz映射以及ℝ n 中的等距和准等距的自然概括。
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