Size of tangencies to non-involutve distributions Zoltan BaloghCornel PinteaHeiner Rohner 58A1028A78Hausdorff dimensiondifferential formsdistributionscontact manifoldsCarnot groups By the classical Frobenius Theorem, a distribution is completely integrable if and only if it is involutive. In this paper, we investigate the size of tangencies of submanifolds with respect to a given \emph{non-involutive} distribution. We provide estimates for the size of the tangency set in terms of its Hausdorff dimension. This generalises earlier works by Derridj and the first author. Our results apply in the setting of contact and symplectic structures as well as of Carnot groups. We illustrate the sharpness of our estimates by a wide range of examples and round the paper off with additional comments and open questions. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.4489 10.1512/iumj.2011.60.4489 en Indiana Univ. Math. J. 60 (2011) 2061 - 2092 state-of-the-art mathematics http://iumj.org/access/