The ∂-problem on Z(q)-domains
Abstract
Given a complex manifold containing a relatively compact Z(q) domain, we give sufficient geometric conditions on the domain so that its L 2 -cohomology in degree ( p, q) (known to be finite-dimensional) vanishes.The condition consists in the existence of a smooth weight function in a neighborhood of the closure of the domain, where the complex Hessian of the weight has a prescribed number of eigenvalues of a particular sign, along with good interaction at the boundary of the Levi form with the complex Hessian, encoded in a subbundle of common positive directions for the two Hermitian forms.
Fields of Study & Subjects
Holomorphic and Operator Theory
Advanced Harmonic Analysis Research
Algebraic and Geometric Analysis
Publication details
- Journal / source
- Pacific Journal of Mathematics
- Volume
- 342
- Issue
- 1
- Pages
- 1–35
- Publication date
- 23 March 2026
- Language
- EN