Nonsingular Ricci flow on a noncompact manifold in dimension three

Li Ma; Anqiang Zhu

doi:10.1016/j.crma.2008.12.002

Topology/Geometry

Nonsingular Ricci flow on a noncompact manifold in dimension three

Presented by: Étienne Ghys

Li Ma ¹; Anqiang Zhu ¹

¹ Department of Mathematical Sciences, Tsinghua University, Peking 100084, PR China

Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 185-190.

Abstract
Résumé

We consider the Ricci flow $\frac{\partial}{\partial t} g = - 2 Ric$ on the 3-dimensional complete noncompact manifold $(M, g (0))$ with nonnegative curvature operator, i.e., $Rm ⩾ 0$ , and $| Rm (p) | \to 0$ , as $d (o, p) \to \infty$ . We prove that the Ricci flow on such a manifold is nonsingular in any finite time.

Nous considérons le flot de Ricci $\frac{\partial}{\partial t} g = - 2 Ric$ sur la variété tridimensionnelle complète de courbure non négatif, c'est-à-dire $Rm ⩾ 0$ et $| Rm (p) | \to 0$ si $d (o, p) \to \infty$ . Nous démontrons que le flot de Ricci sur une telle variété est non singular pour tout temps fini.

Received: 2008-07-07
Accepted: 2008-11-03
Published online: 2009-02-01

DOI: 10.1016/j.crma.2008.12.002

Author's affiliations:

Li Ma ¹; Anqiang Zhu ¹

¹ Department of Mathematical Sciences, Tsinghua University, Peking 100084, PR China

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     author = {Li Ma and Anqiang Zhu},
     title = {Nonsingular {Ricci} flow on a noncompact manifold in dimension three},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {185--190},
     publisher = {Elsevier},
     volume = {347},
     number = {3-4},
     year = {2009},
     doi = {10.1016/j.crma.2008.12.002},
     language = {en},
}

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Li Ma; Anqiang Zhu. Nonsingular Ricci flow on a noncompact manifold in dimension three. Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 185-190. doi : 10.1016/j.crma.2008.12.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.12.002/

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