Rigidity and continuous extension for conformal maps of circle domains. (English) Zbl 1527.30020
The author gives sufficient conditions under which a conformal map between two planar domains has a continuous or homeomorphic extension to the closures of the domains. This interesting work is motivated, in part, by the Koebe conjecture to the effect that every planar domain is conformally equivalent to a domain whose boundary components are circles or points. In the case of domains with countably many boundary components this conjecture was proved by Z.-X. He and O. Schramm [Ann. Math. (2) 137, No. 2, 369–406 (1993; Zbl 0777.30002)].
Reviewer: Matti Vuorinen (Turku)
MSC:
| 30C62 | Quasiconformal mappings in the complex plane |
| 30C65 | Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations |
| 30C35 | General theory of conformal mappings |
Citations:
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