The Levi form for $C^1$-smooth hypersurfaces, and the complex structure on the boundary of domains of holomorphy

A description is given of the set of those boundary points of a domain of holomorphy $D\subset\mathbf C^2$ which have a neighborhood in which the boundary fibers into analytic curves. For domains with $C^1$-smooth boundary whose closure has a basis of Stein neighborhoods this set coincides with the complement of the Shilov boundary $S_{A(\overline D)}$.
Bibliography: 5 titles.