Microlocal pseudoconvexity and ``edge of the wedge'' theorem (Q755945)

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.