Lower bound of admissible functions on the Grassmannian G_m,nm (C)

Abstract

We prove the existence of an "extremal" function lower bounding all admissible functions (ie plurisubharmonic functions modulo a metric) with supremum equal to zero on the complex Grassmann manifold G_m,nm(C). The functions considered are invariant under a suitable automorphisms group. This gives a conceptually simple method to compute Tian's invariant in the case of a non toric manifold.