Analysis and geometry on worm domains
Complex Variables
2007-10-23 v1 Analysis of PDEs
Abstract
We describe recent work on the Bergman kernel of the (non-smooth) worm domain in several complex variables. An asymptotic expansion is obtained for the Bergman kernel. Mapping properties of the Bergman projection are studied. Irregularity properties of the kernal at the boundary are established. This is an expository paper, and considerable background is provided. Discussion of the smooth worm is also included.
Cite
@article{arxiv.0710.4087,
title = {Analysis and geometry on worm domains},
author = {Steven G. Krantz and Marco M. Peloso},
journal= {arXiv preprint arXiv:0710.4087},
year = {2007}
}