Aeppli Cohomology and Gauduchon Metrics

Let (M,J,g,omega) be a complete Hermitian manifold of complex dimension n >= 2 . Let 1 <= p <= n-1 and assume that omega n-p is ( partial differential + partial differential over bar-bounded. We prove that, if psi is an L2 and d-closed (p, 0)-form on M, then psi=0. In particular, if M is compact, we derive that if the Aeppli class of omega n-pvanishes, then HBCp,0(M)=0. As a special case, if M admits a Gauduchon metric omega uch that the Aeppli class of omega n-1 vanishes, then H-BC(1,0)(M)=0}.