Bott-Chern harmonic forms on complete Hermitian manifolds

Let (M, J, g,ω) be a Hermitian manifold of complex dimension n. Assume that the torsion of the Chern connection Δ is bounded, and that there exists a C∞exhausting function ρ : M → R such that Δρ,Δ2ρ are bounded. We characterize W1,2 Bott-Chern harmonic forms, extending the usual result that holds on compact Hermitian manifolds. Finally, if (M,J, g,ω) is Kähler complete, ω = dη, with η bounded, and the sectional curvature is bounded, then we get a vanishing theorem for W1,2 Bott-Chern harmonic (p, q)-forms, if p + q ≠= n.