Mabuchi functional

The Mabuchi functional is an important concept in differential geometry, particularly in the study of Kähler manifolds and the geometric analysis of the space of Kähler metrics. It was introduced by the mathematician Toshiki Mabuchi in the context of Kähler geometry. The Mabuchi functional is a functional defined on the space of Kähler metrics in a fixed Kähler class and is closely related to the notion of Kähler-Einstein metrics.