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

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.

This version contains an update of the Acknowledgements section. 22 pages