Volume 5 Article informations Lower bound of plurisubharmonic functions in G2,5C invariant by a group of automorphisms Riadh JELLOUL Abstract In a previous work [1], I proved the existence of a function minimizing all functions admissible to sup zero on a non-toric algebraic variety namely G2,4C. The functions considered are invariant by a group of automorphisms obtained from that of Pm(C). We prove in this paper that the Tian invariant on the Grassmannian G2,5C is 5=18. The method presented in this article uses a group of automorphisms which operates transitively on G2,5C as well as a dip natural of it in P9C. Keywords: Grassmann manifold, plurisubharmonic function, Tian's invariant.