Convergence and stability of locally \mathbb{R}^{N}-invariant solutions of Ricci flow

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/222187Important models for immortal solutions of Ricci flow that collapse with bounded curvature come from locally G-invariant solutions on principal bundles, where G is a nilpotent Lie group. In this paper, we establish convergence and asymptotic stability, modulo smooth finite-dimensional center manifolds, of certain R^{N}-invariant solutions. When the dimension of the total space is three, these results are relevant to work of Lott classifying the asymptotic behavior of all 3-dimensional Ricci flow solutions whose sectional curvatures and diameters are respectively O(t^{-1}) and O(t^{1/2}).The only revisions are improvements in exposition and notation. To appear in Journal of Geometric AnalysisDifferential GeometryAnalysis of PDEs53C44 (Primary), 58J37 (Secondary)Convergence and stability of locally \mathbb{R}^{N}-invariant solutions of Ricci flowtext