On the asymptotic behavior of expanding gradient Ricci solitons (Q1759652)

Consider an \(n\)-dimensional expanding gradient Ricci soliton \((M,g,f)\) with faster-than-quadratic-decay of curvature, that is, \[ \lim_{\text{dist} (O,x)\rightarrow \infty} |\mathrm{Sect}(x)|\cdot \mathrm{dist}(O,x)^2=0. \] The main result of this paper shows that if \(M\) is simply connected at infinity and \(n\geq 3\), then its tangent cone at infinity must be a manifold isometric to \(\mathbb R^n\).