Taming 3-manifolds using scalar curvature Academic Article uri icon

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 ℝ 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.

author list (cited authors)

  • Chang, S., Weinberger, S., & Yu, G.

citation count

  • 3

complete list of authors

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

publication date

  • October 2010