Convergence of the Ricci flow toward a unique soliton

Natasa Sesum

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Convergence of the Ricci flow toward a unique soliton

Natasa Sesum

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Abstract

We will consider a {\it $τ$-flow}, given by the equation $\frac{d}{dt}g_{ij} = -2R_{ij} + \frac{1}τg_{ij}$ on a closed manifold $M$, for all times $t\in [0,\infty)$. We will prove that if the curvature operator and the diameter of $(M,g(t))$ are uniformly bounded along the flow and if one of the limit solitons is integrable, then we have a convergence of the flow toward a unique soliton, up to a diffeomorphism.

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BibTeX RIS

Natasa Sesum. 2004-05-20. Convergence of the Ricci flow toward a unique soliton. https://arxiv.org/abs/math/0405398

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