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arXiv · 2410.08736

Higher dimensional worm domains

Simone Calamai·Gian Maria Dall'Ara
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Abstract

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.

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Simone Calamai, Gian Maria Dall'Ara. 2024-10-11. Higher dimensional worm domains. https://arxiv.org/abs/2410.08736

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