论文标题
在逆Poletky逆上不平等现象中
On the inverse Poletsky inequality with cotangent dilatation
论文作者
论文摘要
该文章致力于在广泛的映射中建立通道家庭的模量的扭曲，以允许分支点。特别是，对于几乎无处可区分并且具有$ n $ - 和$ n^{\， - 1} $ - luzin属性且在几乎所有路径上绝对连续的映射，我们获得了与所谓的cotangangent膨胀相反的不平等。我们已经证明，对于反映射，这种扩张与相应的反映射的所谓切向膨胀相吻合。此外，我们已经证明，尤其是在阳性lebesgue度量的集合中，cotangengent扩张少于嘴巴或内部扩张。
The article is devoted to establishing the distortion of the modulus of families of paths in wide classes of mappings that admit branch points. In particular, for mappings that are differentiable almost everywhere and have $N$- and $N^{\,- 1}$-Luzin properties and are absolutely continuous on almost all paths, we obtained the inverse Poletsky inequality with the so-called cotangent dilatation. We have proved that, for inverse mappings, this dilatation coincides with the so-called tangential dilatation of the corresponding inverse mapping. In addition, we have proved that cotangent dilatation is less than the outher or inner dilatation, in particular, may be less than one on the set of positive Lebesgue measure
