On a stability property of Skyrme-related energy functionals

TL;DR

This paper investigates the stability of certain critical maps related to Skyrme energy functionals, focusing on symplectic Dirichlet and sigma_2 energies, which are key components in Skyrme sigma-models.

Contribution

It provides a theoretical analysis of the stability properties of critical maps in Skyrme-related energy functionals, highlighting conditions for stability.

Findings

Identifies stability criteria for critical maps under symplectic Dirichlet energy.

Analyzes the role of sigma_2 energy in the stability of Skyrme models.

Contributes to understanding the mathematical structure of Skyrme energy functionals.

Abstract

We study the stability of critical maps from (or into) spheres with respect to the symplectic Dirichlet and $\sigma_2$ energies which are the fourth power terms in Skyrme type sigma-models.