Some results on $p$-harmonic maps from gradient Ricci solitons

Abstract

In this paper, we consider smooth $p$-harmonic maps \linebreak $u:(M^m,g,f) \to (N^n,h)$, where $(M^m,g,f)$ is a gradient Ricci soliton. We provide conditions on the manifolds and the map under which we can obtain the Liouville theorem for $p$-harmonic maps. Additionally, we derive necessary conditions for a map from a gradient Yamabe soliton to be $p$-harmonic.