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
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10.1512/iumj.2011.60.4489
10.1512/iumj.2011.60.4489
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Indiana Univ. Math. J. 60 (2011) 2061 - 2092
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