Liouville properties for \(p\)-harmonic maps with finite \(q\)-energy (Q2796507)

A function \(u\) on a Riemannian manifold \(M\) is said to be \(p\)-harmonic \((p>1)\) whenever it satisfies the equation \(\Delta_p u : = \operatorname{div} (| \nabla u|^{p-2}\nabla u) = 0\). The \(q\)-energy of a function \(u\) is defined by \(E(u) = \int_M |\nabla u|^q d\mathrm{vol}\). The authors provide conditions (a combination of curvature and dimension estimates, relations between \(p\), \(q\) and the dimension of \(M\), and so on) which imply that any \(p\)-harmonic function \(u\) of finite \(q\)-energy on \(M\) is constant.