Geometry & Topology
- Geom. Topol.
- Volume 15, Number 2 (2011), 927-975.
Ricci flow on open $3$–manifolds and positive scalar curvature
We show that an orientable –dimensional manifold admits a complete riemannian metric of bounded geometry and uniformly positive scalar curvature if and only if there exists a finite collection of spherical space-forms such that is a (possibly infinite) connected sum where each summand is diffeomorphic to or to some member of . This result generalises G Perelman’s classification theorem for compact –manifolds of positive scalar curvature. The main tool is a variant of Perelman’s surgery construction for Ricci flow.
Geom. Topol., Volume 15, Number 2 (2011), 927-975.
Received: 10 February 2010
Revised: 25 March 2011
Accepted: 8 May 2011
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60] 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.) 57M50: Geometric structures on low-dimensional manifolds
Bessières, Laurent; Besson, Gérard; Maillot, Sylvain. Ricci flow on open $3$–manifolds and positive scalar curvature. Geom. Topol. 15 (2011), no. 2, 927--975. doi:10.2140/gt.2011.15.927. https://projecteuclid.org/euclid.gt/1513732308