Asian Journal of Mathematics
Volume 19 (2015)
Structure at infinity of expanding gradient Ricci soliton
Pages: 933 – 950
We study the geometry at infinity of expanding gradient Ricci solitons $(M^n, g, \nabla f), n \geq 3$, 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.
Ricci flow, expanding gradient Ricci soliton, asymptotic cone
2010 Mathematics Subject Classification