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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Bloch constants of bounded symmetric domains


Author: Genkai Zhang
Journal: Trans. Amer. Math. Soc. 349 (1997), 2941-2949
MSC (1991): Primary 32H02, 32M15
MathSciNet review: 1329540
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Abstract: Let $D_{1}$ and $D_{2}$ be two irreducible bounded symmetric domains in the complex spaces $V_{1}$ and $V_{2}$ respectively. Let $E$ be the Euclidean metric on $V_{2}$ and $h$ the Bergman metric on $V_{1}$. The Bloch constant $b(D_{1}, D_{2})$ is defined to be the supremum of $E(f^{\prime }(z)x, f^{\prime }(z)x)^{\frac {1}{2}}/h_{z}(x, x)^{1/2}$, taken over all the holomorphic functions $f: D_{1}\to D_{2}$ and $z\in D_{1}$, and nonzero vectors $x\in V_{1}$. We find the constants for all the irreducible bounded symmetric domains $D_{1}$ and $D_{2}$. As a special case we answer an open question of Cohen and Colonna.


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Additional Information

Genkai Zhang
Affiliation: School of Mathematics, University of New South Wales, Kensington NSW 2033, Australia
Address at time of publication: Department of Mathematics, University of Karlstad, S-651 88 Karlstad, Sweden
Email: genkai.zhang@hks.se

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01518-3
PII: S 0002-9947(97)01518-3
Keywords: Bounded symmetric domain, holomorphic mapping, Schwarz lemma, Bergman metric, Bloch constant
Received by editor(s): November 21, 1994
Received by editor(s) in revised form: May 10, 1995
Additional Notes: Research sponsored by the Australian Research Council
Article copyright: © Copyright 1997 American Mathematical Society