On the inverse K i -inequality for one class of mappings


Oleksandr Dovhopiatyi, Evgeny Sevost'yanov




We study mappings differentiable almost everywhere, possessing the N-Luzin property, the N −1-property on the spheres with respect to the (n − 1)-dimensional Hausdorff measure and such that the image of the set where its Jacobian equals to zero has a zero Lebesgue measure. It is proved that such mappings satisfy the lower bound for the Poletsky-type distortion in their definition domain.