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Sur la représentation conforme des surfaces de Riemann à bord et une caractérisation des courbes séparantes
| Content Provider | Semantic Scholar |
|---|---|
| Author | Gabard, Alexandre Pierre Joseph |
| Copyright Year | 2006 |
| Abstract | On presente une demonstration simplifiee d'un theoreme d'Ahlfors: etant donne une courbe algebrique reelle separante, il est toujours possible d'exhiber un morphisme vers la droite dont les fibres au-dessus des points reels sont toutes exclusivement formees de points reels. Ensuite, on montre comment notre methode, basee sur l'usage du theoreme d'Abel, conduit a une meilleure borne sur le degre d'un tel morphisme que celle obtenue par Ahlfors. [We present a simplified proof of a theorem due to Ahlfors: given a dividing real algebraic curve, it is always possible to find a morphism to the line such that the fibers over real points consist only of real points. Then in a second part, we show how our method - which is quite elementary, relying only on the use of Abel's theorem - even leads to a better bound on the degree of such a morphism than the one obtained by Ahlfors.] |
| Starting Page | 945 |
| Ending Page | 964 |
| Page Count | 20 |
| File Format | PDF HTM / HTML |
| DOI | 10.4171/CMH/82 |
| Volume Number | 81 |
| Alternate Webpage(s) | http://www.ems-ph.org/journals/show_pdf.php?iss=4&issn=0010-2571&rank=12&vol=81 |
| Alternate Webpage(s) | https://doi.org/10.4171/CMH%2F82 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
