2008/12/10 by Andrea Young, Young, Andrea
Mathematics · Medicine · #53C07 #53C21 #53C44 (Primary) #58J35 (Secondary) #Advanced Neuroimaging Techniques and Applications #Center manifold #Computer science #Curvature #Differential Geometry (math.DG) #Dimension (graph theory) #Einstein #FOS: Mathematics #Fixed point #Flow (mathematics) #Gauge theory #Geometric Analysis and Curvature Flows #Geometric flow #Geometry #Geometry and complex manifolds #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear system #Physics #Pure mathematics #Ricci curvature #Ricci flow #Stability (learning theory) #Yang–Mills existence and mass gap #math.DG #msc:53C07 #msc:53C21 #msc:53C44 #msc:58J35
paper · pdf · doi:10.48550/arxiv.0812.1823
16 pages
arxiv created 2008/12/10 · openalex publication_date 2008/12/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Let P be a principal U(1)-bundle over a closed manifold M. On P, one can define a modified version of the Ricci flow called the Ricci Yang-Mills flow, due to these equations being a coupling of Ricci flow and the Yang-Mills heat flow. We use maximal regularity theory and ideas of Simonett concerning the asymptotic behavior of abstract quasilinear parabolic partial differential equations to study the stability of the volume-normalized Ricci Yang-Mills flow at Einstein Yang-Mills metrics in dimension two. In certain cases, we show the presence of a center manifold of fixed points, while in others, we show the existence of an asymptotically stable fixed point.