A Family of Lempert Domains

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 \({{\mathbb {L}}}_n\) ${\mathbb{L}}_n$ , \(n\ge 1\) $n\ge 1$ , 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 \({{\mathbb {L}}}_n\) ${\mathbb{L}}_n$ are Lempert domains.