Harmonic maps from smooth metric measure spaces (Q2909613)

The authors consider generalized harmonic maps from a smooth metric measure space \((M,g,e^{-\phi}dv)\) into a Riemannian manifold \((N,h)\), called \(\phi\)-harmonic maps. A \(\phi\)-harmonic map is a critical point of the energy functional \(E_{\phi}\). This is a generalization of harmonic maps from a smooth Riemannian manifold.NEWLINENEWLINERigidity results for \(\phi\)-harmonic maps from a metric measure space with non-negative Bakry-Émery Ricci tensor are proved.NEWLINENEWLINEWe point-out that one of these results generalizes a result of \textit{R. Schoen} and \textit{S.-T. Yau} [Comment. Mat. Helv. 51, 333--341 (1976; Zbl 0361.53040)] in their study of a Liouville type theorem for harmonic maps.