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Bloch constants of bounded symmetric domains

Authors:	Genkai Zhang

Affiliation:	School of Mathematics, University of New South Wales, Kensington NSW 2033, Australia

Abstract:	Let $D_{1}$ and $D_{2}$ be two irreducible bounded symmetric domains in the complex spaces $V_{1}$ and $V_{2}$ respectively. Let be the Euclidean metric on $V_{2}$ and 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 $zin D_{1}$ , and nonzero vectors $xin V_{1}$ . 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.

Keywords:	Bounded symmetric domain holomorphic mapping Schwarz lemma Bergman metric Bloch constant

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