Applications of Bergman representative coordinates

DOI10.1216/rmj.2020.50.631zbMath1442.32003OpenAlexW3030308085MaRDI QIDQ2188456

Steven G. Krantz

Publication date: 11 June 2020

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1590739295

zbMATH Keywords

Bergman kernelBergman metriclinear mappingrepresentative coordinates

Mathematics Subject Classification ID

Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables (32H02) Bergman spaces of functions in several complex variables (32A36) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25) Holomorphic functions of several complex variables (32A10)

Related Items

The Bergman kernel function for intersections of some cylindrical domains and Lauricella's hypergeometric function

Cites Work

• Unnamed Item
• The Bergman kernel on some Hartogs domains
• The geometry of complex domains
• The automorphism groups of strongly pseudoconvex domains
• Normal families and the semicontinuity of isometry and automorphism groups
• Biholomorphic mappings and the \(\overline\partial\)-problem
• On the mapping problem for algebraic real hypersurfaces
• Biholomorphic mappings and the Bergman kernel off the diagonal
• A simplification and extension of Fefferman's theorem on biholomorphic mappings
• An explicit computation of the Bergman kernel function
• Semicontinuity of compact group actions on compact differentiable manifolds
• Deformation of complex structures, estimates for the (partial d) equation, and stability of the Bergman kernel
• The Bergman kernel and biholomorphic mappings of pseudoconvex domains
• Bergman coordinates
• New formulas of the Bergman kernels for complex ellipsoids in $\mathbb {C}^2$
• How to prove Fefferman's theorem without use of differential geometry
• A note on the Bergman kernel