On fillings by holomorphic discs of the levels of a Morse function
A filling by holomorphic discs of the level sets near the critical point of a Morse function on a hypersurface in \(\mathbb{C}^2\) is constructed. The family of discs filling the critical level near its cone point is similar to a Bishop family. It is the uniform limit of the Bishop families filling the level surfaces consisting of two components near their elliptic points and of the families of holomorphic discs filling the levels consisting of one component. For hypersurfaces of contact type near the critical point the regularity of the induced foliation of the pseudoconvex side is shown. This is used to construct smooth, regular extensions with Levi-flat levels of certain Morse functions on (smooth) boundaries of Stein surfaces.
scientific article; zbMATH DE number 1308140
scientific article