In the report, I will talk about estimates for the area of intersection of a surface and a box (cuboid). As an application of these results, for some foliations of hypersurfaces in Carnot groups, an embedding theorem is proved 鈥� the mapping of the sub-Riemannian Sobolev class is locally H枚lder on almost all surfaces under the condition p>谓鈥�1, where 谓 is the homogeneous dimension of the group.
