14 may 2018 -- 15:00
Cortona
Abstract.
The Mabuchi functional is proved to be convex and continuous along a Chen geodesic segment in the space of Kaehler potentials, by the work of Berman-Berndtsson and also Chen-Li-Paun. In this talk, we will discuss the strict convexity of the Mabuchi functional. It is known from Berman example that this strict convexity fails along arbitrary geodesic ray. However, we will prove that it holds when the two boundaries of the geodesic are energy minimizers.