Structure at infinity of expanding gradient ricci soliton

Abstract

We study the geometry at infinity of expanding gradient Ricci solitons (Mn, g,∇f), n ≥ 3, with finite asymptotic curvature ratio without curvature sign assumptions. We mainly prove that they have a noncollapsed cone structure at infinity. Certain topological informations still can be obtained under conditions only involving asymptotic Ricci curvature ratio. Furthermore, we derive a quantitative relationship between (small) asymptotic curvature ratio and asymptotic volume ratio.