Compressed product of balls and lower boundary estimates of Bergman kernels. (English) Zbl 1057.32003
Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 4th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 6–15, 2002. Sofia: Coral Press Scientific Publishing (ISBN 954-90618-4-1/pbk). 193-205 (2003).
The image of a product of balls under a compression
is called a compressed product of balls of exponent .
The author shows that the group of the holomorphic automorphisms and the -orbit structure of is verified by an explicit calculation of the Bergman kernel. As a consequence, local lower boundary estimates of the Bergman kernels of the bounded pseudoconvex domains are obtained, which are locally inscribed in at a common boundary point.
|32A25||Integral representation; canonical kernels (several complex variables)|
|32M05||Complex Lie groups, automorphism groups acting on complex spaces|