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Given a uniform foliation by Gromov hyperbolic leaves on a $3$-manifold, weshow that the action of the fundamental group on the universal circle isminimal and transitive on pairs of different points. We also prove two otherresults: we prove that general uniform Reebless foliations are$\mathbb{R}$-covered and we give a new description of the universal circle of$\mathbb{R}$-covered foliations with Gromov hyperbolic leaves in terms of theJSJ decomposition of $M$.

Minimality of the action on the universal circle of uniform foliations