Friday October 22nd, 2021 | |
| Time: | 10:00 AM |
| Title: | Uniformization of planar domains by exhaustion |
| Speaker: | Kai Rajala, University of Jyvaskyla |
| Location: | Zoom |
| Abstract: | |
| In 1908, Koebe conjectured that every subdomain of the complex plane admits a conformal map onto a circle domain. Koebe verified his conjecture for finitely connected domains, and He and Schramm for countably connected domains. We discuss the method of constructing conformal maps onto circle domains by approximating a given domain with an increasing sequence of finitely connected subdomains and considering the corresponding sequence of conformal maps onto finitely connected circle domains. We show that this method fails if one starts with an arbitrary approximation, but that it works for countably connected domains after small adjustments. | |