On the MMP for rank one foliations on threefolds

Abstract: We prove existence of flips and the base point free theorem for log canonical foliated pairs of rank one on a Q-factorial projective klt threefold. This, in particular, provides a proof of the existence of a minimal model for a rank one foliation on a threefold for a wider range of singularities, after McQuillan. Moreover, we show abundance in the case of numerically trivial log canonical foliated pairs of rank one.