Singular solutions to the Loewner equation
| dc.creator | Prokhorov, Dmitri | |
| dc.creator | Vasil'ev, Alexander | |
| dc.date | 2008-07-03 | |
| dc.date | 2008-09-29 | |
| dc.date.accessioned | 2026-07-07T10:05:36Z | |
| dc.date.available | 2026-07-07T10:05:36Z | |
| dc.description | We consider the Löwner differential equation generating univalent self-maps of the unit disk (or of the upper half-plane). If the solution to this equation represents a one-slit map, then the driving term is a continuous function. The reverse statement is not true in general as a famous Kufarev's example shows. We address the following main problem: to find a criterium for the Löwner equation to generate one-slit solutions. New examples of non-slit solutions to the Löwner equation are presented. Properties of singular slit solutions are revealed. | |
| dc.description | 14 pages, figures are added | |
| dc.identifier | https://arxiv.org/abs/0807.0519 | |
| dc.identifier | http://arxiv.org/abs/0807.0519 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170056 | |
| dc.subject | Complex Variables | |
| dc.subject | 30C35 | |
| dc.title | Singular solutions to the Loewner equation | |
| dc.type | text |