Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 247

On Fillings by Holomorphic Discs of the Levels of a Morse Function

K. Mohnke

A filling by holomorphic discs of the level sets near the critical point is contructed. The so obtained family of discs filling the critical level surface near its conus point similar to a Bishop family is the uniform limit of the Bishop families filling the level surfaces consisting of two cups near their elliptic points and of the families of holomorphic discs filling the levels consisting of a totally real handle. In the case of a hypersurface 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.

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