Enveloppes inferieures de fonctions admissibles sur l'espace projectif complexe. Cas symetrique

Abstract

We prove that admissible functions for Fubini-Study metrics on the complex projective space $P_{m}C$, of complex dimension $m$, invariant by a convenient automorphisms group, are lower bounded by a function going to minus infinity on the boundary of usual charts of $P_{m}C$. A similar lower bound holds on some projective manifolds. This gives an optimal constant in a Hormander type inequality on these manifolds, which allows us to establish the existence of Einstein-Kahler metrics on them.