Comptes Rendus
no. 9
Differential Geometry
Compact blow-up limits of finite time singularities of Ricci flow are shrinking Ricci solitons

Presented by: Étienne Ghys

Zhei-lei Zhang1
1 Chern Institute of Mathematics, Weijin Road 94, Tianjin 300071, PR China
Comptes Rendus. Mathématique, Volume 345 (2007) no. 9, pp. 503-506.

Using the λ and μ functional introduced by Perelman, we prove that the compact blow-up limit of a Ricci flow which generates singularities at finite time must be a shrinking Ricci soliton.

Utilisant les fonctionnelles λ et μ introduites par Perelman, nous démontrons que les limites d'explosion compactes, en temps fini, du flot de Ricci engendrent des singularities de type solitons « rapetissés ».

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.09.017

Zhei-lei Zhang 1

1 Chern Institute of Mathematics, Weijin Road 94, Tianjin 300071, PR China 
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Zhei-lei Zhang. Compact blow-up limits of finite time singularities of Ricci flow are shrinking Ricci solitons. Comptes Rendus. Mathématique, Volume 345 (2007) no. 9, pp. 503-506. doi : 10.1016/j.crma.2007.09.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.09.017/

[1] R.S. Hamilton Three manifolds with positive Ricci curvature, J. Differential Geom., Volume 17 (1982), pp. 255-306

[2] R.S. Hamilton A compactness property for solutions of the Ricci flow, Amer. J. Math., Volume 117 (1995), pp. 545-572

[3] T. Ivey Ricci solitons on compact three-manifolds, Differential Geom. Appl., Volume 3 (1993), pp. 301-307

[4] B. Kleiner; J. Lott Notes on Perelman's paper | arXiv

[5] G. Perelman The entropy formula for the Ricci flow and its geometric applications | arXiv

[6] O.S. Rothaus Logarithmic Sobolev inequalities and the spectrum of Schrödinger operators, J. Funct. Anal., Volume 42 (1981), pp. 110-120

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