arXiv subjects
Publications and source records attributed to Adnene Ben Abdesselem.
This paper generalizes the first author's preceding works concerning admissible functions on certain Fano manifolds. Here, we study a larger class of functions which can be less symmetric than the ones studied before. When the sup of these functions is null, we prove that they admit a lower bound, giving precisely Tian invariant on these manifolds.
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.