Abstract
We establish a new type of the classical boundary Schwarz lemma for holomorphic self-mappings of the unit polydisk Dn in ℂn. By using the Caratheodory metric and Kobayashi metric of Dn, we obtain some properties of the complex Jacobian matrix Jf(p) at a boundary point p of Dn for a holomorphic self-mapping f of Dn. Our results extend the classical Schwarz lemma at the boundary to high dimensions.
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