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
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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
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