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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 Nebenhülle. 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. 2025-06-09. On a higher-dimensional worm domain and its geometric properties. https://doi.org/10.1112/jlms.70195

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