  In this work we establish a gradient bound and Liouville-type theorems for
solutions to Quasi-linear elliptic equations on compact Riemannian Manifolds
with nonnegative Ricci curvature. Also, we provide a local splitting theorem
when the inequality in the gradient bound becomes equality at some point.
Moreover, we prove a Harnack-type inequality and an ABP estimate for the
gradient of solutions in domains contained in the manifold.
