Harmonic maps between 2-dimensional simplicial complexes 2

TL;DR

This paper investigates harmonic maps between 2D simplicial complexes equipped with conformal metrics, establishing foundational existence, uniqueness, and regularity results for such maps in both Euclidean and hyperbolic settings.

Contribution

It extends previous work by proving new existence, uniqueness, and regularity theorems for harmonic maps between conformally related metrics on simplicial complexes.

Findings

Existence of harmonic maps under conformal metrics

Uniqueness of harmonic maps in the given setting

Regularity results for harmonic maps between complexes

Abstract

We study metrics on two-dimensional simplicial complexes that are conformal either to flat Euclidean metrics or to the ideal hyperbolic metrics described by Charitos and Papadopoulos. Extending the results of our previous paper, we prove existence, uniqueness, and regularity results for harmonic maps between two such metrics on a complex.