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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 B p σ ,q of a product of balls B p ×B q under a compression

c σ (X,Y)=(X,V(1- t X ¯X) σ/2 )

is called a compressed product of balls of exponent σ.

The author shows that the group Aut(B p σ ,q ) of the holomorphic automorphisms and the Aut(B p σ ,q )-orbit structure of B p σ ,q 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 B p σ ,q at a common boundary point.

MSC:
32A25Integral representation; canonical kernels (several complex variables)
32M05Complex Lie groups, automorphism groups acting on complex spaces