| Résume | Let (M, g, X) be a complete gradient Kähler-Ricci expander with quadratic curvature decay (including all derivatives). Its geometry at infinity is modeled by a unique asymptotic cone, which takes the form of a Kähler cone (C0, g0). In this talk, we will show that if there exists a solution to the Kähler-Ricci flow on M that desingularizes this cone, then it necessarily coincides with the self-similar solution determined by the soliton metric g. Furthermore, if one perturbs the soliton metric in a suitable manner, the resulting initial data generates an immortal solution to the Kähler-Ricci flow which, after appropriate rescaling, converges to an asymptotically conical gradient Kähler-Ricci expander. |
