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- Title
Global regularity of the $$\overline \partial$$ -neumann problem on an annulus between two pseudoconvex manifolds which satisfy property (P)problem on an annulus between two pseudoconvex manifolds which satisfy property (P).
- Authors
Rae Cho, Hong
- Abstract
Let X be a complex manifold of dimension n≥3. Let Ω, Ω be two open pseudoconvex submanifolds with smooth boundary such that Ω ⋐ Ω ⋐ X . Let Ω = Ω \ $$\overline \Omega_1 $$ . Assume that bΩ and bΩ satisfy Catlin's condition (P). Then the compactness estimate for ( p, q)-forms with 0< q< n−1 holds for the $$\overline \partial$$ -Neumann problem on Ω. This result implies that given a $$\overline \partial$$ -closed ( p, q)-form α with 0< q< n−1, which is C on $$\overline \Omega$$ and which is cohomologous to zero on Ω, the canonical solution u of the equation $$\overline \partial$$ u=α is smooth on $$\overline \Omega$$ .
- Publication
Manuscripta Mathematica, 1996, Vol 90, Issue 1, p437
- ISSN
0025-2611
- Publication type
Article
- DOI
10.1007/BF02568317