Work

Ricci flow on open 3–manifolds and positive scalar curvature

Year: 2011

Type: article

Abstract: We show that an orientable 3-dimensional manifold M admits a complete riemannian metric of bounded geometry and uniformly positive scalar curvature if and only if there exists a finite collection F of spherical space-forms such that M is a (possibly infinite) connected sum where each summand is diffeomorphic to S 2 S 1 or to some member of F .This result generalises G Perelman's classification theorem for compact 3-manifolds of positive scalar curvature.The main tool is a variant of Perelman's surgery construction for Ricci flow.

Source: Geometry & Topology

DOI: 10.2140/gt.2011.15.927

Authors: Laurent Bessières, Gérard Besson, Sylvain Maillot

Institutions: Centre National de la Recherche Scientifique, Université Joseph Fourier, Institut Fourier, Institut Montpelliérain Alexander Grothendieck, Université Montpellier 2

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Agence Nationale de la Recherche

Awards: Flots et opérateurs géométriques, Théorie géométrique des groupes