Hausdorff measure of critical set for Luzin N condition

It is well-known that there a Sobolev homeomorphism f∈W1,p([−1,1]n,[−1,1]n) for any p<n which maps set C of zero Lebesgue n-dimensional measure onto positive measure. We study the size this critical and characterize its lower upper bounds from perspective Hausdorff measures defined by general gauge function.