A Family of Lempert Domains

作者：A. Edigarian · 发表于：Journal of Geometric Analysis · 年份：2023 · DOI：10.1007/s12220-024-01640-7 · 被引用次数：3 · 研究领域：Mathematics

In Ghosh and Zwonek (2-proper holomorphic images of classical Cartan domains. https://doi.org/10.48550/arXiv.2303.11940) introduced a new class of domains Ln\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb {L}}}_n$$\end{document}, n≥1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\ge 1$$\end{document}, which are 2-proper holomorphic images of the Cartan domains of type four. This family contains biholomorphic images of the symmetrized bidisc and the tetrablock. It is well-known, that symmetrized bidisc and tetrablock are Lempert domains. In our paper we show that the whole family of domains Ln\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb {L}}}_n$$\end{document} are Lempert domains.