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Geometry of three-dimensional manifolds with positive scalar curvature

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arxiv 2201.05595 v3 pith:N723KQFD submitted 2022-01-14 math.DG math.AP

Ovidiu Munteanu , Jiaping Wang This is my paper · ORCID
classification math.DGmath.AP
keywords curvaturescalarcasepositivevolumegrowthmanifoldsnonnegative
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The purpose of this paper is to derive volume and other geometric information for three-dimensional complete manifolds with positive scalar curvature. In the case that the Ricci curvature is nonnegative, it is shown that the volume of the manifold must be of linear growth when the scalar curvature is bounded from below by a positive constant. This answers a question of Gromov in the affirmative for dimension three. Volume growth estimates are also obtained for the case when scalar curvature decays to zero. In fact, results of similar nature are established for the more general case that the Ricci curvature is asymptotically nonnegative.

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Cited by 1 Pith paper

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  1. Preserving curvature lower bounds when Ricci flowing non-smooth initial data

    math.DG 2024-11 conditional novelty 1.0 of 10

    A survey of results on Ricci flow from non-smooth initial data, focusing on preservation of lower curvature bounds and open problems.

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