Department of Mathematics, Nanjing Normal University, Nanjing, Jiangsu 210097, People's Republic of China ; Département de Mathématiques et de Statistique, Université de Montréal, Montréal, Québec, Canada H3C 3J7
Abstract:
We give lower estimates for Bloch's constant for quasiregular holomorphic mappings. A holomorphic mapping of the unit ball into is -quasiregular if it maps infinitesimal spheres to infinitesimal ellipsoids whose major axes are less than or equal to times their minor axes. We show that if is a -quasiregular holomorphic mapping with the normalization then the image contains a schlicht ball of radius at least This result is best possible in terms of powers of Also, we extend to several variables an analogous result of Landau for bounded holomorphic functions in the unit disk.