Mathematical Proceedings of the Cambridge Philosophical Society: Volume 123 -

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Mathematical Proceedings of the Cambridge Philosophical Society
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EISSN: 1469-8064

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Volume 123 - January 1998

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CORRIGENDUM

The L2∂-problem on manifolds with piecewise strictly pseudoconvex boundaries
PATRICK DARKO
Published online by Cambridge University Press:

01 January 1998, pp. 191-192
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(Volume 116 (1994), 147–149)
This note is to correct [2], where the proofs of the theorems stated require extra conditions on the manifolds. This is because it is assumed tacitly in [2] that a locally square integrable ∂-closed (p, q)-form on a manifold Ω with a piecewise strictly pseudoconvex boundary is ∂-exact. This is equivalent to Hq(Ω, Dp)=0, q[ges ]1, where Dp is the sheaf of germs of holomorphic p-forms on Ω. This is not true in general, but true if Ω is Stein; but to assume Ω is Stein is too restrictive a condition.

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Volume 123 - January 1998

CORRIGENDUM

The L2∂-problem on manifolds with piecewise strictly pseudoconvex boundaries

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Volume 123 - January 1998

CORRIGENDUM

The L2∂-problem on manifolds with piecewise strictly pseudoconvex boundaries