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Zbl 1057.32003
Kasparian, Azniv
Compressed product of balls and lower boundary estimates of Bergman kernels. (English)
[A] Mladenov, Iva\"ilo 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. 193-205 (2003). ISBN 954-90618-4-1/pbk

The image $B_{p^\sigma,q}$ of a product of balls $B_p\times B_q$ under a compression $$ c_\sigma(X,Y)=(X, V(1-\,^t\bar XX)^{\sigma/2}) $$ is called a compressed product of balls of exponent $\sigma\in {\Bbb R}$. \par The author shows that the group $\Aut(B_{p^\sigma,q})$ of the holomorphic automorphisms and the $\Aut(B_{p^\sigma,q})$-orbit structure of $B_{p^\sigma,q}$ 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 $B_{p^\sigma,q}$ at a common boundary point.
[Der-Chen Chang (Washington D. C.)]

MSC 2000:: *32A25 Integral representation of holomorphic functions (several variables)
32M05 Automorphism groups of complex spaces

Keywords: Bergman kernel; holomorphic automorphisms; estimates

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