2011/09/12 by Liang Cheng, Cheng, Liang, Anqiang Zhu +1
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1109.2443
openalex publication_date 2011/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we investigate the behavior of ADM mass and Einstein-Hilbert functional under the Yamabe flow. Through studying the Yamabe flow by weighted spaces, we show that ADM mass and Einstein-Hilbert functional are well-defined and monotone non-increasing under the Yamabe flow on n-dimensional, n≥ 3, asymptotically flat manifolds. In the case of dimension n=3 or 4, we obtain that the ADM mass is invariant under the Yamabe flow and the Yamabe flow is the gradient flow of Einstein-Hilbert functional on asymptotically flat manifolds