Gradient estimate of a Poisson equation under the almost Ricci solitons

Abstract

In this paper, we consider an n-dimensional manifold M^{n} endowed with an almost Bakry–Émery Ricci curvature and study a special case of gradient estimate for the positive solutions of Delta u-X.u=f, for a smooth function f and a smooth vector field X under the almost Ricci solitons condition.