2022/07/14 by Gilles Carron, Carron, Gilles, Chen, Eric +2
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2207.07003
openalex publication_date 2022/07/14 · openalex created_date 2022/07/16 · openalex updated_date 2026/07/28
We study the Yamabe flow on asymptotically flat manifolds with non-positive Yamabe constant Y≤ 0. Previous work by the second and third named authors \citeChenWang showed that while the Yamabe flow always converges in a global weighted sense when Y>0, the flow must diverge when Y≤ 0. We show here in the Y≤ 0 case however that after suitable rescalings, the Yamabe flow starting from any asymptotically flat manifold must converge to the unique positive function which solves the Yamabe problem on a compactification of the original manifold.