Characterization of Asymptotically Smooth Curves
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909878539255808 |
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| author | Matsuzaki, Katsuhiko Tao, Fei |
| author_facet | Matsuzaki, Katsuhiko Tao, Fei |
| contents | We construct an explicit example of an asymptotically conformal chord-arc curve that fails to be asymptotically smooth. This implies that a function belonging to both the little Bloch space and BMOA does not necessarily lie in VMOA, and that a strongly quasisymmetric homeomorphism which is symmetric is not necessarily strongly symmetric. We also provide a complete characterization of asymptotically smooth curves in terms of asymptotic conformality and uniform approximability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26514 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterization of Asymptotically Smooth Curves Matsuzaki, Katsuhiko Tao, Fei Complex Variables Primary 30C62, 30H35, 30H30, Secondary 46E15, 53A04 We construct an explicit example of an asymptotically conformal chord-arc curve that fails to be asymptotically smooth. This implies that a function belonging to both the little Bloch space and BMOA does not necessarily lie in VMOA, and that a strongly quasisymmetric homeomorphism which is symmetric is not necessarily strongly symmetric. We also provide a complete characterization of asymptotically smooth curves in terms of asymptotic conformality and uniform approximability. |
| title | Characterization of Asymptotically Smooth Curves |
| topic | Complex Variables Primary 30C62, 30H35, 30H30, Secondary 46E15, 53A04 |
| url | https://arxiv.org/abs/2510.26514 |