On a higher-dimensional worm domain and its geometric properties
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\"ulle. We also show that their Bergman projections do not preserve the Sobolev space for sufficiently large Sobolev indices.
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