English

On a higher-dimensional worm domain and its geometric properties

Complex Variables 2025-06-10 v2

Abstract

We construct new 33-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

R2 v1 2026-06-28T16:57:16.377Z