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

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

2003-05-20

arxiv.org/abs/math/0305291v1

Mathematics

Differential Geometry

article of 14 pages

Scientific paper

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.

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