On sequences of maps with equibounded energies

Let X, Y be two oriented Riemannian manifolds respectively of dimensions n, m greater than or equal to 2. We shall assume that Y is compact and withou t boundary and that its integral 2-homology group H-2(Y) has no torsion, so that H-2(Y, Z) = {Sigma ((s) over bar)(s=1) n(s)[gamma](s)}, gamma (1),.., gamma ((s) over bar) being integral cycles and H-2(Y, R) = H-2(Y, Z) XR, a nd for future use eve denote by omega (1),..., omega ((s) over bar) the har monic forms such that integral (gammas) omega (r) = ([gamma (s)]R\[omega (r)]) = deltas(r).