Balanced homogeneous harmonic maps between cones

TL;DR

This paper investigates the degrees of homogeneous harmonic maps between simplicial cones, linking their properties to eigenvalues of graph Laplacians, to understand regularity in harmonic maps between singular spaces.

Contribution

It introduces a study of homogeneous harmonic maps between cones and connects their degrees to graph Laplacian eigenvalues, advancing understanding of harmonic map regularity.

Findings

Degrees of homogeneous harmonic maps relate to eigenvalues of graph Laplacians.

Provides insights into local behavior of harmonic maps in singular spaces.

Establishes a connection between geometric analysis and spectral graph theory.

Abstract

We study the degrees of homogeneous harmonic maps between simplicial cones. Such maps have been used to model the local behavior of harmonic maps between singular spaces, where the degrees of homogeneous approximations describe the regularity of harmonic maps. In particular the degrees of homogeneous harmonic maps are related to eigenvalues of discrete normalized graph Laplacians.