1-convex manifolds are p-Kähler

We study here Kähler-type properties of 1-convex manifolds, using the duality between forms and compactly supported currents, and some properties of the Aeppli groups of q-convex manifolds. We prove that, when the exceptional set S of the 1-convex manifold X has dimension k, X is p-Kähler for every p > k, and is k-Kähler if and only if "the fundamental class" of S does not vanish. There are classical examples where X is not k-Kähler even with a smooth S, but we prove that this cannot happen if 2k ≥ n = dim X, nor for suitable neighborhoods of S; in particular, X is always balanced (i.e., (n - 1)-Kähler).