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

Dan Knopf

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arXiv · 0711.3859

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

Dan Knopf

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Abstract

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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Dan Knopf. 2009-03-05. Convergence and stability of locally \mathbb{R}^{N}-invariant solutions of Ricci flow. https://arxiv.org/abs/0711.3859

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