On a class of complete non-compact gradient Yamabe solitons

2011/09/05 by Jia-Yong Wu, Wu, Jia-Yong
Mathematics · #55Q52 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #Primary 53C21 #Secondary 53C44

paper · pdf · doi:10.48550/arxiv.1109.0861

openalex publication_date 2011/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive lower bounds on the scalar curvature of complete non-compact gradient Yamabe solitons under some integral curvature conditions. Based on this, we prove that the corresponding potential functions have at most quadratic growth in distance. We also obtain a finite topological type property on complete shrinking gradient Yamabe solitons under suitable scalar curvature assumptions.

Citations

• On the parabolic kernel of the Schrödinger operator
• Differential equations on riemannian manifolds and their geometric applications
• The classification of locally conformally flat Yamabe solitons

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• Complete Yamabe solitons with finite total scalar curvature
• Remarks on scalar curvature of Yamabe solitons
• A note on compact gradient Yamabe solitons
• Triviality results for compact k-Yamabe solitons