Closed Range for ∂ and ∂b on Bounded Hypersurfaces in Stein Manifolds

الأصل · EN

We define weak Z(q), a generalization of Z(q) on bounded domains Ω in a Stein manifold Mⁿ that suffices to prove closed range of ∂. Under the hypothesis of weak Z(q), we also show (i) that harmonic (0,q)-forms are trivial and (ii) if ∂Ω satisfies weak Z(q) and weak Z(n-1-q), then has closed range on (0,q)-forms on ∂Ω. We provide examples to show that our condition contains examples that are excluded from (q-1)-pseudoconvexity and the authors' previous notion of weak Z(q).