On CR maps from the sphere into the tube over the future light cone II: Higher dimensions

We determine all CR maps from the sphere in $\mathbb{C}^3$ into the tube over the future light cone in $\mathbb{C}^4$. This result leads to a complete characterization of proper holomorphic maps from the three-dimensional unit ball into the classical domain of type IV of four dimension and confirms a conjecture of Reiter - Son in [26] from 2022. Additionally, we prove a boundary characterization of isometric holomorphic embeddings from a ball into a classical domain of type IV in arbitrary dimensions that is similar to the main result in Huang - Lu - Tang - Xiao [16]. The result is then used to treat a special case in the general characterization.