Consider the energy $E_\lambda(u)=\int |du|^2 +\lambda \int |u*\omega_{S^2}|^2$ among maps $u\colon S^3\to S^2$, where $\omega_{S^2}$ is the volume form on $S^2$. The Hopf fibration is a linearly stable critical point for all $\lambda \geq 1/2$. In a joint work with A. Guerra and K. Zemas, we show that it is a minimizer in its homotopy class for large enough $\lambda$.