| Résume | Kähler-Ricci solitons are a natural generalization of the concept of a Kähler-Einstein metric which arise in the study of the Kähler-Ricci flow. In particular, shrinking gradient Kähler-Ricci solitons on non-compact manifolds model the singularity development of the Kähler-Ricci flow. In this talk, I will present some of my thesis work on the uniqueness of shrinking gradient Kähler-Ricci solitons on non-compact toric manifolds. In particular, the standard product of the Fubini-Study metric on CP¹ (the round metric on S²) and the Euclidean metric on C is the only shrinking gradient Kähler-Ricci soliton on CP¹ x C with bounded scalar curvature. |
