Long-time behavior of 3–dimensional Ricci flow, D : Proof of the main results

Bamler, Richard¹

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

Geometry & topology, Tome 22 (2018) no. 2, pp. 949-1068.

Résumé

This is the fourth and last part of a series of papers on the long-time behavior of $3$–dimensional Ricci flows with surgery. In this paper, we prove our main two results. The first result states that if the surgeries are performed correctly, then the flow becomes nonsingular eventually and the curvature is bounded by $C{t}^{-1}$. The second result provides a qualitative description of the geometry as $t\to \infty$.

Détail

DOI : 10.2140/gt.2018.22.949

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

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