Quasiconformal extension for harmonic mappings on finitely connected domains
We prove that a harmonic quasiconformal mapping defined on a finitely connected domain in the plane, all of whose boundary components are either points or quasicircles, admits a quasiconformal extension to the whole plane if its Schwarzian derivative is small. We also make the observation that a uni...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2021-09-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.233/ |
| _version_ | 1797651564903530496 |
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| author | Efraimidis, Iason |
| author_facet | Efraimidis, Iason |
| author_sort | Efraimidis, Iason |
| collection | DOAJ |
| description | We prove that a harmonic quasiconformal mapping defined on a finitely connected domain in the plane, all of whose boundary components are either points or quasicircles, admits a quasiconformal extension to the whole plane if its Schwarzian derivative is small. We also make the observation that a univalence criterion for harmonic mappings holds on uniform domains. |
| first_indexed | 2024-03-11T16:16:37Z |
| format | Article |
| id | doaj.art-c632df84bd0f4d328f3ca9d943800928 |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:16:37Z |
| publishDate | 2021-09-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj.art-c632df84bd0f4d328f3ca9d9438009282023-10-24T14:19:25ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692021-09-01359790590910.5802/crmath.23310.5802/crmath.233Quasiconformal extension for harmonic mappings on finitely connected domainsEfraimidis, Iason0https://orcid.org/0000-0002-0252-5607Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, TX 79409, United States.We prove that a harmonic quasiconformal mapping defined on a finitely connected domain in the plane, all of whose boundary components are either points or quasicircles, admits a quasiconformal extension to the whole plane if its Schwarzian derivative is small. We also make the observation that a univalence criterion for harmonic mappings holds on uniform domains.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.233/ |
| spellingShingle | Efraimidis, Iason Quasiconformal extension for harmonic mappings on finitely connected domains Comptes Rendus. Mathématique |
| title | Quasiconformal extension for harmonic mappings on finitely connected domains |
| title_full | Quasiconformal extension for harmonic mappings on finitely connected domains |
| title_fullStr | Quasiconformal extension for harmonic mappings on finitely connected domains |
| title_full_unstemmed | Quasiconformal extension for harmonic mappings on finitely connected domains |
| title_short | Quasiconformal extension for harmonic mappings on finitely connected domains |
| title_sort | quasiconformal extension for harmonic mappings on finitely connected domains |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.233/ |
| work_keys_str_mv | AT efraimidisiason quasiconformalextensionforharmonicmappingsonfinitelyconnecteddomains |