Isometries in the diamond

Abstract

We show the (anti)holomorphicity of smooth Kobayashi isometries of the diamond, the domain defined as $△:=\{z\in {\mathbb{C}}^2:|z_1|+|z_2|<1\}$. Additionally, we discuss the problem of uniqueness of real geodesics, left inverses and strict convexity of indicatrices.

15 pages