An existence and uniqueness result for orientation-reversing harmonic diffeomorphism from $\mathbb{H}_*^n$ to $\mathbb{R}_*^n$

TL;DR

This paper establishes an existence and uniqueness theorem for orientation-reversing harmonic diffeomorphisms with rotational symmetry from hyperbolic to Euclidean space in higher dimensions, extending known 2D results.

Contribution

It generalizes the 2D existence and uniqueness results for harmonic diffeomorphisms to higher dimensions with rotational symmetry.

Findings

Proves existence of orientation-reversing harmonic diffeomorphisms in higher dimensions.

Establishes uniqueness of these diffeomorphisms under symmetry conditions.

Extends classical 2D results to n-dimensional hyperbolic and Euclidean spaces.

Abstract

In this paper, we prove an existence and uniqueness theorem for orientation-reversing harmonic diffeomorphisms from $\mathbb{H}_*^n$ to $\mathbb{R}_*^n$ with rotational symmetry, which is a generalization of the corresponding result for dimension $2$.