Schwarz Lemma at the Boundary on the Classical Domain of Type III Citation： Taishun LIU,Xiaomin TANG,Wenjun ZHANG.Schwarz Lemma at the Boundary on the Classical Domain of Type III[J].Chinese Annals of Mathematics B,2020,41(3):335~360 Page view： 131        Net amount： 87 Authors： Taishun LIU; Xiaomin TANG;Wenjun ZHANG Foundation： This work was supported by the National Natural Science Foundation of China (Nos.11571105, 11771139). Abstract： Let $\mathcal{R_\mathcal{\uppercase\expandafter{\romannumeral3}}}(n)$ be the classical domain of type $\mathcal{\uppercase\expandafter{\romannumeral3}}$ with $n\geq 2$. This article is devoted to a deep study of the Schwarz lemma on $\mathcal{R_\mathcal{\uppercase\expandafter{\romannumeral3}}}(n)$ via not only exploring the smooth boundary points of $\mathcal{R_\mathcal{\uppercase\expandafter{\romannumeral3}}}(n)$ but also proving the Schwarz lemma at the smooth boundary point for holomorphic self-mappings of $\mathcal{R_\mathcal{\uppercase\expandafter{\romannumeral3}}}(n)$. Keywords： Holomorphic mapping, Schwarz lemma at the boundary, The classicaldomain of type $mathcal{uppercaseexpandafter{romannumeral3}}$ Classification： 32H02, 32H99, 30C80 Download PDF Full-Text