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

Published online by Cambridge University Press:  01 January 1998

PATRICK DARKO
PATRICK DARKO
Affiliation:
Department of Mathematics, Howard University, Washington D.C. 20059, U.S.A.
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Abstract

(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.

Type
CORRIGENDUM
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 123 , Issue 1 , January 1998 , pp. 191 - 192
Copyright
Cambridge Philosophical Society 1998

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