Conformal mappings on the Grushin plane
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866916260354195456 |
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| author | Walicki, Marcin |
| author_facet | Walicki, Marcin |
| contents | We study conformal mappings in the Grushin plane and provide a number of their characterizations in terms of the Sobolev mappings and their geometry. Furthermore, we connect conformality on the Grushin plane with conformality on the complex plane by using the Meyerson map. Among applications we discuss admissible curves and length-distortion estimates in the Grushin plane, as well as the Carathéodory extension theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_10111 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Conformal mappings on the Grushin plane Walicki, Marcin Complex Variables Metric Geometry 30C20 (Primary) 53C17 (Secondary) We study conformal mappings in the Grushin plane and provide a number of their characterizations in terms of the Sobolev mappings and their geometry. Furthermore, we connect conformality on the Grushin plane with conformality on the complex plane by using the Meyerson map. Among applications we discuss admissible curves and length-distortion estimates in the Grushin plane, as well as the Carathéodory extension theorem. |
| title | Conformal mappings on the Grushin plane |
| topic | Complex Variables Metric Geometry 30C20 (Primary) 53C17 (Secondary) |
| url | https://arxiv.org/abs/2309.10111 |