Higher dimensional worm domains
Complex Variables
2024-10-15 v2
Abstract
We show how to construct a class of smooth bounded pseudoconvex domains whose boundary contains a given Stein manifold with strongly pseudoconvex boundary, having a prescribed codimension and D'Angelo class (a cohomological invariant measuring the "winding" of the boundary of the domain around the submanifold). Some open questions in the regularity theory of the -Neumann problem are discussed in the setting of these domains.
Keywords
Cite
@article{arxiv.2410.08736,
title = {Higher dimensional worm domains},
author = {Simone Calamai and Gian Maria Dall'Ara},
journal= {arXiv preprint arXiv:2410.08736},
year = {2024}
}
Comments
12 pages. Minor corrections/clarifications: higher regularity of the submanifold needed for Sard theorem to work; domains are smooth in Section 5