We study the Bloch constant for K-quasiconformal holomorphic mappings of the unit ball B of C<sup>n</sup> into C<sup>n</sup>. The final result we prove in this paper is: If f is a K-quasiconfor...We study the Bloch constant for K-quasiconformal holomorphic mappings of the unit ball B of C<sup>n</sup> into C<sup>n</sup>. The final result we prove in this paper is: If f is a K-quasiconformal holomorphic mapping of B into C<sup>n</sup> such that det（f’（0））=1, then f（B） contains a schlicht ball of radius at least （C<sub>n</sub>K）<sup>1-n</sup> integral from n=0 to 1(（1+t）<sup>n-1</sup>/（1-t）<sup>2</sup> exp{-（n+1）t/（1-t）}dt, where C<sub>n</sub>】1 is a constant depending on n only, and C<sub>n</sub>→10<sup>1/2</sup> as n→∞.展开更多
基金Research supported in part by NSFC (China)JNSF (Jiangsu).
文摘We study the Bloch constant for K-quasiconformal holomorphic mappings of the unit ball B of C<sup>n</sup> into C<sup>n</sup>. The final result we prove in this paper is: If f is a K-quasiconformal holomorphic mapping of B into C<sup>n</sup> such that det（f’（0））=1, then f（B） contains a schlicht ball of radius at least （C<sub>n</sub>K）<sup>1-n</sup> integral from n=0 to 1(（1+t）<sup>n-1</sup>/（1-t）<sup>2</sup> exp{-（n+1）t/（1-t）}dt, where C<sub>n</sub>】1 is a constant depending on n only, and C<sub>n</sub>→10<sup>1/2</sup> as n→∞.
