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arXiv · 2406.04905

On a higher-dimensional worm domain and its geometric properties

Steven G. Krantz·Marco M. Peloso·Caterina Stoppato
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Abstract

We construct new $3$-dimensional variants of the classical Diederich-Fornaess worm domain. We show that they are smoothly bounded, pseudoconvex, and have nontrivial Nebenh\"{u}lle. We also show that their Bergman projections do not preserve the Sobolev space for sufficiently large Sobolev indices.

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Steven G. Krantz, Marco M. Peloso, Caterina Stoppato. 2024-06-07. On a higher-dimensional worm domain and its geometric properties. https://doi.org/10.1112/jlms.70195

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