Suites de flots de Ricci en dimension 3 et applications

Thomas Richard

doi:10.5802/tsg.281

Thomas Richard ¹

¹ Université Grenoble 1 Institut Fourier 100 rue des Maths BP 74 8402 St Martin d’Hères cedex (France)

Séminaire de théorie spectrale et géométrie, Volume 28 (2009-2010), pp. 121-145.

Abstract
Résumé

In this article, we review some results of Miles Simon about the Ricci flow of some 3-dimensional metric spaces. These results are from [26] and [28]. We first explain the link between rigidity theorems and convergence of manifolds on an example from Berger and Durumeric. Then, we notice that in order to obtain such rigidity theorems using Ricci flow, one needs to build a Ricci flow for potentially non-smooth spaces. The last two sections expose how to construct such flows (following [26] and [28]) and give some geometric applications of this construction.

Dans cet article, on passe en revue certains résultats dus à Miles Simon sur le flot de Ricci de certains espaces métriques de dimension 3 exposés dans [28] et [26].

On commence par voir le lien entre théorèmes de rigidité et convergence des variétés sur un exemple dû à Berger et Durumeric. On remarque ensuite que pour obtenir de tels théorèmes de rigidité en utilisant le flot de Ricci, il faut être capable de construire le flot pour des espaces peu lisses.

Les deux dernières partie sont consacrées à une explication de la construction de tels flots (en suivant [28] et [26]) et à des applications géométriques de cette construction.

DOI: 10.5802/tsg.281

Classification: 53C44, 53C20, 53C23
Mot clés : courbure de Ricci minorée, flot de Ricci, convergence au sens de Gromov-Hausdorff, dimension 3
Keywords: Ricci curvature bounded from below, Ricci flow, Gromov-Hausdorff convergence, dimension 3

Author's affiliations:

Thomas Richard ¹

¹ Université Grenoble 1 Institut Fourier 100 rue des Maths BP 74 8402 St Martin d’Hères cedex (France)

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Thomas Richard. Suites de flots de Ricci en dimension 3 et applications. Séminaire de théorie spectrale et géométrie, Volume 28 (2009-2010), pp. 121-145. doi : 10.5802/tsg.281. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.281/

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