Enveloppes inférieures de fonctions admissibles sur l'espace projectif complexe. Cas symétrique |
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Authors: | A. Ben Abdesselem |
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Affiliation: | Institut Mathématique de Jussieu UMR 9994, Paris, LIM, École Polytechnique de Tunisie, Tunisie |
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Abstract: | We prove that admissible functions for Fubini-Study metric on the complex projective space PmC 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 PmC. A similar lower bound holds on some projective manifolds. This gives an optimal constant in a Hörmander type inequality on these manifolds, which allows us, using Tian's invariant, to establish the existence of Einstein-Kähler metrics on them. |
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Keywords: | 53C55 58G30 |
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