On a higher-dimensional worm domain and its geometric properties
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912420086153216 |
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| author | Krantz, Steven G. Peloso, Marco M. Stoppato, Caterina |
| author_facet | Krantz, Steven G. Peloso, Marco M. Stoppato, Caterina |
| contents | We construct new $3$-dimensional variants of the classical Diederich-Fornaess worm domain. We show that they are smoothly bounded, pseudoconvex, and have nontrivial Nebenhülle. We also show that their Bergman projections do not preserve the Sobolev space for sufficiently large Sobolev indices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04905 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a higher-dimensional worm domain and its geometric properties Krantz, Steven G. Peloso, Marco M. Stoppato, Caterina Complex Variables 32T20 (Primary) 32T05, 32A25, 32A36 (Secondary) We construct new $3$-dimensional variants of the classical Diederich-Fornaess worm domain. We show that they are smoothly bounded, pseudoconvex, and have nontrivial Nebenhülle. We also show that their Bergman projections do not preserve the Sobolev space for sufficiently large Sobolev indices. |
| title | On a higher-dimensional worm domain and its geometric properties |
| topic | Complex Variables 32T20 (Primary) 32T05, 32A25, 32A36 (Secondary) |
| url | https://arxiv.org/abs/2406.04905 |