Classification of asymptotically conical 2D shrinking gradient Kähler-Ricci solitons

Alix Deruelle (Sorbonne Universite Paris)




Abstract: 
Shrinking gradient Kaehler-Ricci solitons are finite time singularity models of the Kaehler-Ricci flow. 
Their classification is central to continue the flow in a canonical way. We focus here on such 
self-similarities which are asymptotically conical and we show that in complex dimension 2, only 
two such solutions exist: the Gaussian shrinking soliton on the 2-complex space and the 
U(2)-invariant shrinking gradient Ricci soliton of Feldman-Ilmanen-Knopf on the blow-up of 
the 2-complex space at one point. 

The lecture is about joint work with Ronan Conlon (FIU Miami) and Song Sun (Berkeley).