On a higher-dimensional worm domain and its geometric properties
Complex Variables
2025-06-10 v2
Abstract
We construct new -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.
Keywords
Cite
@article{arxiv.2406.04905,
title = {On a higher-dimensional worm domain and its geometric properties},
author = {Steven G. Krantz and Marco M. Peloso and Caterina Stoppato},
journal= {arXiv preprint arXiv:2406.04905},
year = {2025}
}
Comments
31 pages, 2 figures