Taming 3-manifolds using scalar curvature Academic Article

abstract

• In this paper we address the issue of uniformly positive scalar curvature on noncompact 3-manifolds. In particular we show that the Whitehead manifold lacks such a metric, and in fact that is the only contractible noncompact 3-manifold with a metric of uniformly positive scalar curvature. We also describe contractible noncompact manifolds of higher dimension exhibiting this curvature phenomenon. Lastly we characterize all connected oriented 3-manifolds with finitely generated fundamental group allowing such a metric. 2009 Springer Science+Business Media B.V.

authors

• Yu, Guoliang

published proceedings

• Geometriae Dedicata

author list (cited authors)

• Chang, S., Weinberger, S., & Yu, G.

citation count

• 8

complete list of authors

• Chang, Stanley||Weinberger, Shmuel||Yu, Guoliang

publication date

• October 2010

publisher

• Springer Nature  Publisher

published in

• Geometriae Dedicata  Journal

keywords

• 49 Mathematical Sciences
• 4902 Mathematical Physics
• 4904 Pure Mathematics

Digital Object Identifier (DOI)

• 10.1007/s10711-009-9402-1

start page

• 3

end page

• 14

volume

• 148

issue

• 1

URL

• http://dx.doi.org/10.1007/s10711-009-9402-1