A collar neighborhood theorem for a complex manifold (Q1332493)

The main result of the paper states that for a domain \(D\) in a smooth paracompact manifold \(\Omega\) of dimension \(2n\) (\(n \geq 2\)), if \(J_ 0 : T\Omega \to T\Omega\) is a smooth almost complex structure on \(\Omega\) formally integrable on \(\overline{D}\), if the boundary \(M\) of \(D\) is strictly pseudoconvex with respect to \(J_ 0\), then one may find an open submanifold \(\omega\) of \(\Omega\) containing \(\overline{D}\) and a complex structure \(J : T\omega \to T\omega\) such that \(J|_ D = J_ 0|_ D\). However, such a collar neighbourhood \(\omega\) may not be unique, as an example, presented by the authors, shows.