Estimates on the non-compact expanding gradient Ricci solitons

In this paper, we deal with the complete non-compact expanding gradient Ricci soliton (Mⁿ,g) with positive Ricci curvature. On the condition that the Ricci curvature is positive and the scalar curvature approaches 0 towards infinity, we derive a useful estimate on the growth of potential functions. Based on this and under the same assumptions, we prove that ∫^t₀ Rc (γ'(s) , γ' (s))ds and ∫^t₀ Rc (γ' (,s). v)ds at least have linear growth, where 7(5) is a minimal normal geodesic emanating from the point where R obtains its maximum. Furthermore, some other results on the Ricci curvature are also obtained.