# Foliations associated to harmonic maps and some complex two ball quotients

## TL;DR

This paper investigates foliations linked to low-rank harmonic maps between complex balls, providing insights into the rigidity properties of certain complex ball quotients.

## Contribution

It introduces a new foliation construction associated with lattice-equivariant harmonic maps and explores their implications for the rigidity of complex ball quotients.

## Key findings

- Established a connection between harmonic maps and foliations in complex balls.
- Proved rigidity results for specific complex ball quotients.
- Analyzed the structure of foliations arising from low-rank harmonic maps.

## Abstract

The purpose of the article is to study a foliation associated to a lattice-equivariant harmonic map of small rank from a complex ball to another. The result is related to rigidity of some complex ball quotients.