A Note on the cone of mobile curves

S. Boucksom, J.-P. Demailly, M. Paun and Th. Peternell proved that the cone of mobile curves ME ( X ) ¯ of a projective complex manifold X is dual to the cone generated by classes of effective divisors and conjectured an extension of this duality in the Kahler set-up. We show that their conjecture implies that ME ( X ) ¯ coincides with the cone of integer classes represented by closed positive smooth ( n − 1 , n − 1 ) -forms. Without assuming the validity of the conjecture we prove that this equality of cones still holds at the level of degree functions.