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arXiv · 1112.3637

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

Michele Rimoldi·Giona Veronelli
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Abstract

In this paper we give some results on the topology of manifolds with $\infty$-Bakry-\'Emery 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.

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Michele Rimoldi, Giona Veronelli. 2011-12-15. Topology of steady and expanding gradient Ricci solitons via f-harmonic maps. https://doi.org/10.1016/j.difgeo.2013.06.001

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