Long time behaviour of Ricci flow on open 3-manifolds

Laurent Bessières (1) , Gérard Besson (2) , Sylvain Maillot (3)

1 IMB - Institut de Mathématiques de Bordeaux
2 IF - Institut Fourier
3 I3M - Institut de Mathématiques et de Modélisation de Montpellier

We study the long time behaviour of Ricci flow with bubbling-off on a possibly noncompact $3$-manifold of finite volume whose universal cover has bounded geometry. As an application, we give a Ricci flow proof of Thurston's hyperbolisation theorem for $3$-manifolds with toral boundary that generalizes Perelman's proof of the hyperbolisation conjecture in the closed case.

Mots clés: open 3-manifolds; hyperbolisation; Ricci flow with surgery

Domaines: Géométrie différentielle [math.DG]

Laurent Bessières, Gérard Besson, Sylvain Maillot. Long time behaviour of Ricci flow on open 3-manifolds. Commentarii Mathematici Helvetici, 2015, 90 (2), pp.377-405. ⟨10.4171/CMH/357⟩. ⟨hal-00730466v2⟩