Long-time behavior of 3–dimensional Ricci flow : introduction

Bamler, Richard¹

¹ Department of Mathematics, University of California, Berkeley, CA, United States

Geometry & topology, Tome 22 (2018) no. 2, pp. 757-774.

Résumé

In the following series of papers we analyze the long-time behavior of $3$–dimensional Ricci flows with surgery. Our main result will be that if the surgeries are performed correctly, then only finitely many surgeries occur and after some time the curvature is bounded by $C{t}^{-1}$. This result confirms a conjecture of Perelman. In the course of the proof, we also obtain a qualitative description of the geometry as $t\to \infty$.

Détail

DOI : 10.2140/gt.2018.22.757

Classification : 53C44, 49Q05, 53C23, 57M15, 57M20, 57M50
Keywords: Ricci flow, Ricci flow with surgery, finitely many surgeries, asymptotics of Ricci flow, $3$–manifolds, geometrization of $3$–manifolds

Bibliographie

[1] R Bamler, Long-time behavior of 3–dimensional Ricci flow, A : Generalizations of Perelman’s long-time estimates, Geom. Topol. 22 (2018)

[2] R Bamler, Long-time behavior of 3–dimensional Ricci flow, B : Evolution of the minimal area of simplicial complexes under Ricci flow, Geom. Topol. 22 (2018)

[3] R Bamler, Long-time behavior of 3–dimensional Ricci flow, C : 3–manifold topology and combinatorics of simplicial complexes in 3–manifolds, Geom. Topol. 22 (2018)

[4] R Bamler, Long-time behavior of 3–dimensional Ricci flow, D : Proof of the main results, Geom. Topol. 22 (2018)

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