The weak min-max property in Banach spaces. (English) Zbl 1511.30008
Since their introduction in 1978 as a tool for studying injectivity theorems in \(\mathbb{R}^n\), uniform domains have been successfully applied in classical function theory, quasiconformal mappings, and other fields of mathematical analysis.
Motivated by previous results of Rasila and Zhou, the authors introduce a new condition which the call the weak min-max property, and use it to characterize diameter uniform domains in Banach spaces of dimension at least 2. As a consequence of their main results, the authors also prove that diameter uniform domains are invariant under relatively quasimöbius mappings.
Motivated by previous results of Rasila and Zhou, the authors introduce a new condition which the call the weak min-max property, and use it to characterize diameter uniform domains in Banach spaces of dimension at least 2. As a consequence of their main results, the authors also prove that diameter uniform domains are invariant under relatively quasimöbius mappings.
Reviewer: Emil Saucan (Karmiel)
MSC:
| 30C65 | Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations |
| 30C20 | Conformal mappings of special domains |
References:
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