Hodge spectral sequence on pseudoconvex domains
The authors' main result is Theorem 4.3: Let \((M,ds^ 2_ M)\) be a Kähler manifold of dimension n and let D be a relatively compact pseudoconvex domain in M with \(C^{\infty}\)-smooth boundary. Suppose that the corank of the Levi form of \(\partial D\) is \(<k\) everywhere on \(\partial D\). Then \[ H^ r(D,{\mathbb{C}})\cong \oplus_{p+q=r}H^{p,q}(D),\quad r\leq n+k;\quad H^{p,q}(D)\cong H^{q,p}(D),\quad p+q\leq n+k. \] This theorem, combined with Andreotti- Grauert's isomorphism theorem on q-convex spaces, implies the theorem of the first-named author [Invent. Math. 63, 335-354 (1981; Zbl 0457.32007)], which is analogue of Hodge's theorem on pseudoconvex manifolds.
scientific article; zbMATH DE number 4040293
scientific article