Bi-Hölder extensions of quasi-isometries on complex domains

Jinsong Liu HLM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China Hongyu Wang HLM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China Qingshan Zhou School of Mathematics and Big Data, Foshan university, Foshan 528000, Guangdong, China

Complex Variables and Complex Analysis mathscidoc:2203.08009

The Journal of Geometric Analysis, 32, (38), 2022.1
In this paper, we prove some results on bi-Hölder extensions not only for biholomorphisms but also for more general Kobayashi metric quasi-isometries between the domains. Furthermore, we establish the Gehring–Hayman type theorems on certain complex domains which play an important role through the paper. Then by applying the above results, we show the bi-Hölder equivalence between the Euclidean boundary and the Gromov boundary of bounded convex domains which are Gromov hyperbolic with respect to their Kobayashi metrics.
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@inproceedings{jinsong2022bi-hölder,
  title={Bi-Hölder extensions of quasi-isometries on complex domains},
  author={Jinsong Liu, Hongyu Wang, and Qingshan Zhou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220317151300842939989},
  booktitle={The Journal of Geometric Analysis},
  volume={32},
  number={38},
  year={2022},
}
Jinsong Liu, Hongyu Wang, and Qingshan Zhou. Bi-Hölder extensions of quasi-isometries on complex domains. 2022. Vol. 32. In The Journal of Geometric Analysis. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220317151300842939989.
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