Abstract
This paper generalizes the first author's preceding works concerning admissible functions on certain Fano manifolds [A. Ben Abdesselem, Lower bound of admissible functions on sphere, Bull. Sci. Math. 126 (2002) 675-680 [2]; A. Ben Abdesselem, Enveloppes infericures de fonctions admissibles sur l'espace projectif complexe. Cas symetrique, Bull. Sci. Math. 130 (2006) 341-353 [3]]. 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 [G. Tian, On Kahler-Einstein metrics on certain Kahler manifolds with C-1 (M) > 0, Invent. Math. 89 (1987) 225-246 [7]] (see also [T. Aubin, Reduction du cas positif de l'equation de Monge-Ampere sur les varietes Kahleriennes a la demonstration d'une inegalite, J. Funct. Anal. 57 (1984) 143-153 [11]) on these manifolds. (C) 2007 Elsevier Masson SAS. Tous droits reserves.