# Harmonic maps from the product of the hyperbolic planes to the hyperbolic space

## TL;DR

This paper proves an existence theorem for harmonic maps from the product of hyperbolic planes to hyperbolic space, addressing the asymptotic Dirichlet problem with boundary data at infinity.

## Contribution

It establishes the existence of harmonic maps in a new geometric setting involving products of hyperbolic planes and hyperbolic space.

## Key findings

- Existence of harmonic maps from product hyperbolic planes to hyperbolic space
- Solution to the asymptotic Dirichlet problem with boundary data at infinity
- Extension of harmonic map theory to product hyperbolic geometries

## Abstract

An existence result is shown for the asymptotic Dirichlet problem for harmonic maps from the product of the hyperbolic planes to the hyperbolic space, where the Dirichlet data is given on the distinguished boundary (the product of the circles at infinity).