A Horrocks' theorem for reflexive sheaves

In this paper, we define m-tail reflexive sheaves as reflexive sheaves on projective spaces with the simplest possible cohomology. We prove that the rank of any m-tail reflexive sheaf E on Pn is greater or equal to nm−m. We completely describe m-tail reflexive sheaves on Pn of minimal rank and we construct huge families of m-tail reflexive sheaves of higher rank.