Complex dimensions of real manifolds, attached analytic discs and parametric argument principle [article]

Mark Agranovsky
2007 arXiv   pre-print
Let Ω be a smooth real analytic submanifold of a complex manifold X. We establish and study the link between the following 3 subjects: 1) topological properties of smooth families of attached analytic discs, the manifold Ω admits, 2) lower bounds for dimensions of complex tangent spaces of Ω, 3) a generalization of the argument principle for smooth families of holomorphic mappings from the standard complex disc to X. In particular, we obtain characterization of complex manifolds and their
more » ... ries in terms of attached analytic discs. The special case when Ω is the graph, leads to new characterizations of holomorphic and CR functions, and in particular, to solutions of some open problems about such functions.
arXiv:0704.2871v2 fatcat:bh5cei7tm5g3jcksakxnmgqj6m