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Taming 3-manifolds using scalar curvature

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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 \({\mathbb{R}^3}\) 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.

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Authors and Affiliations

  1. Department of Mathematics, Wellesley College, Wellesley, MA, 02481, USA

    Stanley Chang

  2. Department of Mathematics, University of Chicago, Chicago, IL, 60637, USA

    Shmuel Weinberger

  3. Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA

    Guoliang Yu

Authors
  1. Stanley Chang
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  2. Shmuel Weinberger
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  3. Guoliang Yu
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Corresponding author

Correspondence to Shmuel Weinberger.

Additional information

Research partially supported by NSF Grants DMS-0405867, DMS-0805913 and DMS-0600216.

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Chang, S., Weinberger, S. & Yu, G. Taming 3-manifolds using scalar curvature. Geom Dedicata 148, 3–14 (2010). https://doi.org/10.1007/s10711-009-9402-1

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  • DOI: https://doi.org/10.1007/s10711-009-9402-1

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