Microlocal pseudoconvexity and “edge of the wedge” theorem. (English) Zbl 0722.32012

Schapira, Pierre; Trepreau, Jean-Marie

Duke Math. J. 61, No. 1, 105-118 (1990).

At first, the authors prove that, for a bounded pseudoconvex domain \(\Omega\) in \({\mathbb{C}}^ n\) with real analytic boundary \(\partial \Omega\) and an open subset \(\omega\) of \(\partial \Omega\), \(\Omega\cup \omega\) has a fundamental system of pseudoconvex neighbourhoods. They consider a complex manifold X, its real analytic generic submanifold of codimension d, an open subset U of the conormal bundle \(T_ N*X\), the Levi form of N having r negative eigenvalues, and the Sato’s microlocalization \(\mu_ N({\mathcal O}_ X)\). They prove the flabbyness of the sheaf \(H^{d+r}(\mu_ N({\mathcal O}_ X))\) under the assumption that U contains no germ of complex curve.

Reviewer: J.Kajiwara (Fukuoka)

MSC:

32T99	Pseudoconvex domains
32C35	Analytic sheaves and cohomology groups
58J15	Relations of PDEs on manifolds with hyperfunctions

Keywords:

Sato’s microlocalization

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