Higher dimensional worm domains
| Autor: | Calamai, Simone, Dall'Ara, Gian Maria |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 12 pages. Minor corrections/clarifications: higher regularity of the submanifold needed for Sard theorem to work; domains are smooth in Section 5 |
| Databáze: | arXiv |
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