Topology of steady and expanding gradient Ricci solitons via f-harmonic maps

Abstract

In this paper we give some results on the topology of manifolds with $\infty$-Bakry-Émery Ricci tensor bounded below, and in particular of steady and expanding gradient Ricci solitons. To this aim we clarify and further develop the theory of f-harmonic maps from non-compact manifolds into non-positively curved manifolds. Notably, we prove existence and vanishing results which generalize to the weighted setting part of Schoen and Yau's theory of harmonic maps.

20 pages. The title has changed in this final version. To appear in Differential Geometry and its Applications

Cited by in corpus (3)

• Stability properties and topology at infinity of f-minimal hypersurfaces
• On $f$-bi-harmonic maps between Riemannian manifolds
• Liouville theorems for $f$-harmonic maps into Hadamard spaces