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 Nebenhülle. We also show that their Bergman projections do not preserve the Sobolev space for sufficiently large Sobolev indices.

31 pages, 2 figures

References in corpus (6)

• Irregularity of the Bergman projection on worm domains in C^n
• Bergman kernel and projection on the unbounded worm domain
• Essential norm estimates for the $\bar{\partial }$-Neumann operator on convex domains and worm domains
• Completeness on the worm domain and the Müntz-Szász problem for the Bergman space
• Worm domains are not Gromov hyperbolic
• Irregularity of the Bergman projection on smooth unbounded worm domains