Schwarz lemma at the boundary of the unit polydisk in C^n  被引量:6

Schwarz lemma at the boundary of the unit polydisk in C^n

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作  者:TANG XiaoMin LIU TaiShun LU Jin 

机构地区:[1]Department of Mathematics, Huzhou Teachers College

出  处:《Science China Mathematics》2015年第8期1639-1652,共14页中国科学:数学(英文版)

基  金:supported by National Natural Science Foundation of China(Grant Nos.11101139,11271124 and 11301136);Natural Science Foundation of Zhejiang Province(Grant No.LY14A010017);Natural Science Foundation of Hebei Province(Grant No.A2014205069)

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

关 键 词:holomorphic mapping Schwarz lemma at the boundary unit polydisk 

分 类 号:O174.5[理学—数学] TP391.41[理学—基础数学]

 

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