On fillings by holomorphic discs of the levels of a Morse function
type: Item
instance of: scholarly article
title: On fillings by holomorphic discs of the levels of a Morse function
zbMATH Open document ID: 0928.32007
DOI: 10.1016/S0926-2245(98)00029-1
author: Klaus Mohnke
published in: Differential Geometry and its Applications
publication date: 2000-01-03T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 32E20
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 1308140
zbMATH Keywords: hull of holomorphy
zbMATH Keywords: holomorphic discs
Wikidata QID: Q115337462
MaRDI profile type: Publication
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full work available at URL: s0926-2245(98)00029-1
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description: scientific article; zbMATH DE number 1308140