Analysis and geometry on worm domains

Details Analysis and geometry on worm domains Analysis and geometry on worm domains

2007-10-22

arxiv.org/abs/0710.4087v1

Mathematics

Complex Variables

Scientific paper

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.

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