Global minimality of the Hopf map in the Faddeev-Skyrme model with large coupling constant

TL;DR

This paper proves that the Hopf map uniquely minimizes the Faddeev--Skyrme energy in its homotopy class under certain geometric conditions, establishing its global minimality.

Contribution

It demonstrates the global minimality of the Hopf map in the Faddeev--Skyrme model for large coupling constants, under specific geometric constraints.

Findings

Hopf map is the unique energy minimizer in its homotopy class

Minimality holds when the target sphere's radius exceeds the domain sphere's radius

The result applies modulo rigid motions, emphasizing symmetry considerations

Abstract

We prove that, modulo rigid motions, the Hopf map is the unique minimizer of the Faddeev--Skyrme energy in its homotopy class, provided that the radius of the target 2-sphere is not smaller than the radius of the domain 3-sphere.