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

TL;DR

This paper classifies all CR maps from the 3-sphere into a specific tube domain, characterizes proper holomorphic maps between certain classical domains, and confirms a recent conjecture, advancing understanding of complex geometric mappings.

Contribution

It provides a complete classification of CR maps from the sphere in three complex dimensions into the tube over the future light cone, and characterizes proper holomorphic maps into classical type IV domains, confirming a 2022 conjecture.

Findings

Classified all CR maps from the sphere in C^3 to the tube over the future light cone.

Characterized proper holomorphic maps from the 3D unit ball into type IV classical domains.

Confirmed a conjecture of Reiter - Son from 2022.

Abstract

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.