Vol. 302, No. 1, 2019

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Schwarz lemma at the boundary on the classical domain of type $\mathcal{IV}$

Jianfei Wang, Taishun Liu and Xiaomin Tang

Vol. 302 (2019), No. 1, 309–334
Abstract

Let V(n) be the classical domain of type V in n with n 2. The purpose of this paper is twofold. The first is to investigate the boundary points of V(n). We give a sufficient and necessary condition such that the boundary points of V(n) are smooth. The second is to establish the boundary Schwarz lemma on the classical domain of type V. we obtain the optimal estimates of the eigenvalues of the Fréchet derivative for holomorphic self-mappings at the smooth boundary point of V(n).

Keywords
holomorphic mapping, Schwarz lemma at the boundary, the classical domain of type $\mathcal{IV}$
Mathematical Subject Classification 2010
Primary: 32H02
Secondary: 32H99, 30C80
Milestones
Received: 2 May 2018
Revised: 13 August 2018
Accepted: 20 January 2019
Published: 5 November 2019
Authors
Jianfei Wang
School of Mathematical Sciences
Huaqiao University
Quanzhou, Fujian
China
Taishun Liu
Department of Mathematics
Huzhou Teachers College, Huzhou University
Zhejiang
China
Xiaomin Tang
Department of Mathematics
Huzhou Teachers College, Huzhou University
Zhejiang
China