Inserted: 20 dec 2011
Last Updated: 22 dec 2011
In this paper we study $f$-harmonic maps from non-compact manifolds into non-positively curved ones. Notably, we prove existence and vanishing results which generalize to the weighted setting part of Schoen and Yau's theory of harmonic maps. As an application, we deduce information on the topology of manifolds with lower bounded $\infty$-Bakry-Emery Ricci tensor, and in particular of steady and expanding gradient Ricci solitons.
Keywords: f-harmonic maps, weighted manifolds, gradient Ricci solitons