The Lempert Theorem and the Tetrablock

In this paper we show that the Lempert property (i.e., the equality between the Lempert function and the Carathéodory distance) holds in the tetrablock, a bounded hyperconvex domain which is not biholomorphic to a convex domain. The question whether such an equality holds was posed by Abouhajar et al. in J. Geom. Anal. 17(4), 717–750 (2007).