Quantitative correspondence between quasi-symmetric mappings on complete metric spaces and rough quasi-isometric mappings on their hyperbolic fillings
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915588644798464 |
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| author | Huang, Manzi Wang, Xiantao Wang, Zhuang Xu, Zhihao |
| author_facet | Huang, Manzi Wang, Xiantao Wang, Zhuang Xu, Zhihao |
| contents | In this paper, we establish a quantitative correspondence between power quasi-symmetric mappings on complete metric spaces and rough quasi-isometric mappings on their hyperbolic fillings. In particular, we prove that the exponents in the power quasi-symmetric mappings coincide with the coefficients in the rough quasi-isometric mappings. This shows that the obtained correspondence is both sharp and consistent. In this way, we generalize the corresponding result by Björn, Björn, Gill, and Shanmugalingam (J. Reine Angew. Math., 2017) from the setting of rooted trees to that of hyperbolic fillings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27523 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantitative correspondence between quasi-symmetric mappings on complete metric spaces and rough quasi-isometric mappings on their hyperbolic fillings Huang, Manzi Wang, Xiantao Wang, Zhuang Xu, Zhihao Complex Variables Primary: 30L10, Secondary: 30L05, 51M10 In this paper, we establish a quantitative correspondence between power quasi-symmetric mappings on complete metric spaces and rough quasi-isometric mappings on their hyperbolic fillings. In particular, we prove that the exponents in the power quasi-symmetric mappings coincide with the coefficients in the rough quasi-isometric mappings. This shows that the obtained correspondence is both sharp and consistent. In this way, we generalize the corresponding result by Björn, Björn, Gill, and Shanmugalingam (J. Reine Angew. Math., 2017) from the setting of rooted trees to that of hyperbolic fillings. |
| title | Quantitative correspondence between quasi-symmetric mappings on complete metric spaces and rough quasi-isometric mappings on their hyperbolic fillings |
| topic | Complex Variables Primary: 30L10, Secondary: 30L05, 51M10 |
| url | https://arxiv.org/abs/2510.27523 |