Complex dimensions of real manifolds, attached analytic discs and parametric argument principle
| dc.creator | Agranovsky, Mark | |
| dc.date | 2007-04-23 | |
| dc.date | 2007-09-05 | |
| dc.date.accessioned | 2026-07-07T08:27:22Z | |
| dc.date.available | 2026-07-07T08:27:22Z | |
| dc.description | 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 boundaries 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. | |
| dc.identifier | https://arxiv.org/abs/0704.2871 | |
| dc.identifier | http://arxiv.org/abs/0704.2871 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137248 | |
| dc.subject | Complex Variables | |
| dc.subject | 32V10, 20E25 | |
| dc.title | Complex dimensions of real manifolds, attached analytic discs and parametric argument principle | |
| dc.type | text |