Quasiconformal contact foliations.

We show that every quasiconformal contact foliation supports an invariant metric and characterise these foliations by the dynamical property of C 1 -equicontinuity. We prove that a generalisation of the Weinstein conjecture holds for quasiconformal contact foliations, and provide a lower bound to the number of closed leaves. In particular, we show that the Weinstein conjecture holds for quasiconformal Reeb fields. [ABSTRACT FROM AUTHOR]