Calculus of Variations and Geometric Measure Theory
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M. Rimoldi - G. Veronelli

$f$-Harmonic maps and applications to gradient Ricci solitons

created by veronelli on 20 Dec 2011
modified by rimoldi on 22 Dec 2011


Submitted Paper

Inserted: 20 dec 2011
Last Updated: 22 dec 2011

Year: 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


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