Scalar Curvature via Local Extent
2018 ◽
Vol 6
(1)
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pp. 146-164
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AbstractWe give a metric characterization of the scalar curvature of a smooth Riemannian manifold, analyzing the maximal distance between (n + 1) points in infinitesimally small neighborhoods of a point. Since this characterization is purely in terms of the distance function, it could be used to approach the problem of defining the scalar curvature on a non-smooth metric space. In the second part we will discuss this issue, focusing in particular on Alexandrov spaces and surfaces with bounded integral curvature.
2013 ◽
Vol 1
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pp. 200-231
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2005 ◽
Vol 15
(4)
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pp. 589-606
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2012 ◽
Vol 6
(4)
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pp. 245-251
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1993 ◽
Vol 131
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pp. 127-133
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1985 ◽
Vol 38
(1)
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pp. 118-129
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