2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67519We 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.article of 14 pagesDifferential Geometry53C55, 58G30text