Bloch constants of bounded symmetric domains

Author:
Genkai Zhang

Journal:
Trans. Amer. Math. Soc. **349** (1997), 2941-2949

MSC (1991):
Primary 32H02, 32M15

DOI:
https://doi.org/10.1090/S0002-9947-97-01518-3

MathSciNet review:
1329540

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Abstract: Let and be two irreducible bounded symmetric domains in the complex spaces and respectively. Let be the Euclidean metric on and the Bergman metric on . The Bloch constant is defined to be the supremum of , taken over all the holomorphic functions and , and nonzero vectors . We find the constants for all the irreducible bounded symmetric domains and . 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:
https://doi.org/10.1090/S0002-9947-97-01518-3

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