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

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

2007-11-24

arxiv.org/abs/0711.3859v2

Mathematics

Differential Geometry

The only revisions are improvements in exposition and notation. To appear in Journal of Geometric Analysis

Scientific paper

Important 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}).

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