Foliations, slope stability, and positivity of log canonical bundles on Deligne-Mumford stacks

We generalize some results of Campana-Păun regarding foliations, slope stability, and positivity of log canonical bundles on smooth projective varieties to the case of smooth proper DM stacks admitting projective coarse moduli spaces. This paper is the third in a series aiming to generalize results of Popa-Schnell and Wei-Wu on Viehweg hyperbolicity to the setting of DM stacks, and in particular, to certain KSBA moduli spaces.