A criterion for the Neumann type problem over a differential complex on a strongly pseudoconvex domain (Q1057401)

This article is one of a series of articles published by the author on this subject. In 1981, the author proved the existence of a versal family of CR structures for the case \(n\geq 4\) [Invent. Math. 63, 311-334 (1981; Zbl 0496.32015)], and in 1982 he showed the existence of a versal family of strongly pseudoconvex domains for the case of dimension \(\geq 5\) [ibid. 68, 317-352 (1982)]. Here the author constructs a versal family of pseudoconvex domains for the four dimensional case. - The proof here has been made easier to follow. The author develops a criterion with which he obtains the new Neumann operator satisfying a suitable condition on the boundary, which in turn leads to the construction of a versal family of strongly pseudoconvex domains for the case \(n\geq 4\).