Bordered Riemann surfaces in C^2
| dc.creator | Forstneric, Franc | |
| dc.creator | Wold, Erlend Fornaess | |
| dc.date | 2007-08-21 | |
| dc.date | 2008-10-02 | |
| dc.date.accessioned | 2026-07-07T12:34:39Z | |
| dc.date.available | 2026-07-07T12:34:39Z | |
| dc.description | One of the oldest open problems in the classical function theory is whether every open Riemann surface admits a proper holomorphic embedding into C^2. In this paper we prove the following Theorem: If D is a bordered Riemann surface whose closure admits an injective immersion in C^2 that is holomorphic in D, then D admits a proper holomorphic embedding in C^2. The most general earlier results are due to J. Globevnik and B. Stensones (Math. Ann. 303 (1995), 579-597) and E. F. Wold (Internat. J. Math. 17 (2006), 963-974). We give an explicit and elementary construction that does not require the Teichmuller space theory, and we also indicate another possible proof using the latter theory. | |
| dc.description | 24 pages, 2 figures. To appear in J. Math. Pure Appl | |
| dc.identifier | https://arxiv.org/abs/0708.2887 | |
| dc.identifier | http://arxiv.org/abs/0708.2887 | |
| dc.identifier | J. Math. Pures Appl. 91 (2009), no. 1, 100-114 | |
| dc.identifier | doi:10.1016/j.matpur.2008.09.010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/217509 | |
| dc.subject | Complex Variables | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 32C22, 32E10, 32H05, 32M17 (Primary); 14H55 (Secondary) | |
| dc.title | Bordered Riemann surfaces in C^2 | |
| dc.type | text |