Schwarz Lemma at the Boundary on the Classical Domain of Type $\mathcal{III}$

Abstract

Let $\mathcal{R}_\mathcal{III}(n)$ be the classical domain of type $\mathcal{III}$ with n ≥ 2. This article is devoted to a deep study of the Schwarz lemma on $\mathcal{R}_\mathcal{III}(n)$ via not only exploring the smooth boundary points of $\mathcal{R}_\mathcal{III}(n)$) but also proving the Schwarz lemma at the smooth boundary point for holomorphic self-mappings of $\mathcal{R}_\mathcal{III}(n)$.

Keywords

Holomorphic mapping / Schwarz lemma at the boundary / The classical domain of type $\mathcal{III}$

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