It is shown that mappings in Rn with finite distortion of area in all dimensions 1 k n1 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Rn中所有尺寸为1 k n1的区域具有有限变形的映射，在映射的内部和外部扩张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-Lipschitz映射的一类，它是bi-Lipschitz映射以及Rn中的等距和准等距的自然概括。
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