论文标题
自由准世界中的gromov双曲线。我
Gromov hyperbolicity in the free quasiworld. I
论文作者
论文摘要
借助统一结构域的格罗莫夫双曲表征，我们首先对Väisälä在较弱的假设下提出的一个开放问题给出了肯定的答案。接下来，我们表明，Väisälä引入的三点条件对于以定量方式获得有限连接的空间之间的quasimöbius图是quasimöbius图。基于这两个结果，我们研究了在Banach空间的统一域上自由地准文献和准纤维映射的边界行为，并部分回答了Väisälä提出的另一个问题，以不同的方式提出。
With the aid of a Gromov hyperbolic characterization of uniform domains, we first give an affirmative answer to an open question arisen by Väisälä under weaker assumption. Next, we show that the three-point condition introduced by Väisälä is necessary to obtain quasisymmetry for quasimöbius maps between bounded connected spaces in a quantitative way. Based on these two results, we investigate the boundary behavior of freely quasiconformal and quasihyperbolic mappings on uniform domains of Banach spaces and partially answer another question raised by Väisälä in different ways.
