  In this paper, by slightly modifying Li-Yau's technique so that we can handle
drifting Laplacians, we were able to find three different gradient estimates
for the warping function, one for each sign of the Einstein constant of the
fiber manifold. As an application, we exhibit a nonexistence theorem for
gradient almost Ricci solitons possessing certain metric properties on the base
of the warped product.

Differential Geometry