A remark on the energy of harmonic maps between spheres (Q1087198)

Let \(\phi: S^ n\to S^ p\) \((n\geq 3)\) be a non-null homotopic harmonic map, and G the group of orientation preserving conformal diffeomorphisms of \(S^ n\). Then \[ \int | d\phi |^ 2=\max_{g\in G}\int | d(\phi \circ g)|^ 2 \geq n \text{vol} S^ n. \]