Gradient estimate of a Poisson equation under the almost Ricci solitons

Abstract

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

Keywords

• Sobolev constant
• Gradient estimate
• Almost Ricci soliton