Taming 3-manifolds using scalar curvature |
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Authors: | Stanley Chang Shmuel Weinberger Guoliang Yu |
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Institution: | 1.Department of Mathematics,Wellesley College,Wellesley,USA;2.Department of Mathematics,University of Chicago,Chicago,USA;3.Department of Mathematics,Vanderbilt University,Nashville,USA |
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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
\mathbbR3{\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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Keywords: | |
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