2011/08/31 by Li Ma, Ma, Li, Vicente Miquel +1 · 1 citation
Mathematics · Physics and Astronomy · #35Jxx #53Qxx #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1108.6212
openalex publication_date 2011/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider the scalar curvature of Yamabe solitons. In particular we show that, with natural conditions and non positive Ricci curvature, any complete Yamabe soliton has constant scalar curvature, namely, it is a Yamabe metric. We also show that the quadratic decay at infinity of the Ricci curvature of a complete non-compact Yamabe soliton has non-negative scalar curvature. A new proof of Kazdan-Warner condition is also presented.