Analysis and geometry on worm domains

2007/10/22 by Steven G. Krantz, Krantz, Steven G., Marco M. Peloso +1 · 1 citation
Engineering · Mathematics · #32F17 #32T20 #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.0710.4087

openalex publication_date 2007/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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