How frequently can Sobolev maps distort the Hausdorff dimension? First part.

Bi-Lipchitz maps between metric spaces do not change the Hausdorff dimension of sets, while Hölder continuous maps distort dimension in a controlled way. In this talk we will consider this type of questions for the class of Sobolev mappings in the setting of foliated metric spaces. The results come from recent joint works with R. Monti, J. Tyson, K. Wildrick.