On the inverse $K_I$-inequality for one class of mappings

Abstract

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.