The Lempert theorem and the tetrablock

TL;DR

This paper proves that the Lempert theorem, which equates the Lempert function and Carathéodory distance, holds in the tetrablock, a specific non-convex hyperconvex domain.

Contribution

It establishes the validity of the Lempert theorem in the tetrablock, expanding understanding of complex analysis in non-convex domains.

Findings

Lempert theorem holds in the tetrablock.

Tetrablock is not biholomorphic to a convex domain.

The result extends the applicability of the Lempert theorem.

Abstract

In the paper we show that the Lempert theorem (i.e. the equality between the Lempert function and the Carath\'eodory distance) holds in the tetrablock, a bounded hyperconvex domain which is not biholomorphic to a convex domain.