Higher dimensional worm domains
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914971243249664 |
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| author | Calamai, Simone Dall'Ara, Gian Maria |
| author_facet | Calamai, Simone Dall'Ara, Gian Maria |
| contents | We show how to construct a class of smooth bounded pseudoconvex domains whose boundary contains a given Stein manifold with strongly pseudoconvex boundary, having a prescribed codimension and D'Angelo class (a cohomological invariant measuring the "winding" of the boundary of the domain around the submanifold). Some open questions in the regularity theory of the $\overline\partial$-Neumann problem are discussed in the setting of these domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08736 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher dimensional worm domains Calamai, Simone Dall'Ara, Gian Maria Complex Variables 32T20, 32W05 We show how to construct a class of smooth bounded pseudoconvex domains whose boundary contains a given Stein manifold with strongly pseudoconvex boundary, having a prescribed codimension and D'Angelo class (a cohomological invariant measuring the "winding" of the boundary of the domain around the submanifold). Some open questions in the regularity theory of the $\overline\partial$-Neumann problem are discussed in the setting of these domains. |
| title | Higher dimensional worm domains |
| topic | Complex Variables 32T20, 32W05 |
| url | https://arxiv.org/abs/2410.08736 |