2014/03/04 by Alexander Brudnyi, A. Brudnyi, Brudnyi, A. +3
Mathematics · #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #Geometry and complex manifolds #math.CV #msc:32A38 #msc:32K99
paper · pdf · doi:10.48550/arxiv.1403.0967
arxiv created 2014/03/04 · arxiv updated 2014/03/06
The classical result of J.J. Kohn asserts that over a relatively compact subdomain D with C^∞ boundary of a Hermitian manifold whose Levi form has at least n-q positive eigenvalues or at least q+1 negative eigenvalues at each boundary point, there are natural isomorphisms between the (p,q) Dolbeault cohomology groups defined by means of C^∞ up to the boundary differential forms on D and the (finite-dimensional) spaces of harmonic (p,q)-forms on D determined by the corresponding complex Laplace operator. In the present paper, using Kohn's technique, we give a similar description of the (p,q) Dolbeault cohomology groups of spaces of differential forms taking values in certain (possibly infinite-dimensional) holomorphic Banach vector bundles on D. We apply this result to compute the (p,q) Dolbeault cohomology groups of some regular coverings of D defined by means of C^∞ forms constrained along fibres of the coverings.