一致整环的齐莫比乌斯不变性
Quasimöbius invariance of uniform domains
摘要：
本文研究了巴拿赫空间中一致域的拟莫比乌斯不变性。我们首先研究了巴拿赫空间中域的某些几何性质的含义，如（直径）一致性，$δ$ -一致性和最小-最大性质。然后，我们证明了所有这些条件是等价的，如果域是$ψ$ -自然的。作为应用，我们部分回答了Väisälä提出的一个公开问题，并给出了一种新的方法来证明M. Huang，Y.黄氏Y. Li，M. Vuorinen和X. Wang在[On quasimöbius maps in real巴拿赫空间，Israel J. Math. 198（2013），467-486]中，这也回答了Väisälä提出的另一个问题。
英文摘要：
In this paper, we study quasimöbius invariance of uniform domains in Banach spaces. We first investigate implications of certain geometric properties of domains in Banach spaces, such as the (diameter) uniformity, the $δ$-uniformity and the min-max property. Then we show that all of these conditions are equivalent if the domain is $ψ$-natural. As applications, we answer partially to an open question proposed by Väisälä, and provide a new method to prove a recent result of M. Huang, Y. Li, M. Vuorinen, and X. Wang in [On quasimöbius maps in real Banach spaces, Israel J. Math. 198 (2013), 467-486], which also gives an answer to another question raised by Väisälä.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
