Gromov hyperbolicity in the free quasiworld. I
Gromov hyperbolicity in the free quasiworld. I
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DOI：
10.4064/sm210825-7-3
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Ponnusamy Saminathan
中科院分区：
文献类型：
--
作者：
Zhou Qingshan;Ponnusamy Saminathan
With the aid of a Gromov hyperbolic characterization of uniform domains, we first give an affirmative answer to an open question arisen by V\"ais\"al\"a under weaker assumption. Next, we show that the three-point condition introduced by V\"ais\"al\"a is necessary to obtain quasisymmetry for quasim\"obius 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 V\"ais\"al\"a in different ways.
