Long time behaviour of Ricci flow on open 3-manifolds

TL;DR

This paper investigates the long-term evolution of Ricci flow with bubbling-off on noncompact 3-manifolds of finite volume, providing a new proof of Thurston's hyperbolisation theorem using Ricci flow techniques.

Contribution

It offers a Ricci flow-based proof of Thurston's hyperbolisation theorem for 3-manifolds with toral boundary, extending Perelman's approach to noncompact cases.

Findings

Proves long-time existence and behavior of Ricci flow on certain noncompact 3-manifolds.

Establishes a Ricci flow proof of Thurston's hyperbolisation theorem for manifolds with boundary.

Abstract

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.