Propagation of boundary CR foliations and Morera type theorems for manifolds with attached analytic discs
| dc.creator | Agranovsky, Mark | |
| dc.date | 2005-11-07 | |
| dc.date | 2006-09-19 | |
| dc.date.accessioned | 2026-07-07T06:50:48Z | |
| dc.date.available | 2026-07-07T06:50:48Z | |
| dc.description | We prove that generic homologically nontrivial $(2n-1)$-parameter family of analytic discs attached by their boundaries to a CR manifold $Ω$ in $\mathbb C^n, n \le 2$ tests CR functions: if a smooth function on $Ω$ extends analytically inside each analytic disc then it satisfies the tangential CR equations. In particular, we answer, in real analytic category, two open questions: on characterization of analytic functions in planar domains (the strip-problem), and on characterization of boundary values of holomorphic functions in domains in $\mathbb C^n$ (a conjecture of Globevnik and Stout). We also characterize complex curves in $\mathbb C^2$ as real 2-manifolds admitiing homologically nontrivial 1-parameter families of attached analytic discs. The proofs are based on reduction to a problem of propagation of degeneracy of CR foliations of torus-like manifolds. | |
| dc.description | The version accepted in Advances in Mathematics | |
| dc.identifier | https://arxiv.org/abs/math/0511125 | |
| dc.identifier | http://arxiv.org/abs/math/0511125 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104781 | |
| dc.subject | Complex Variables | |
| dc.subject | 32V10; 20E25 | |
| dc.title | Propagation of boundary CR foliations and Morera type theorems for manifolds with attached analytic discs | |
| dc.type | text |