Scalar Curvature via Local Extent
We 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 th...
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-11-01
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| Series: | Analysis and Geometry in Metric Spaces |
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| Online Access: | https://doi.org/10.1515/agms-2018-0008 |
| _version_ | 1818909230155956224 |
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| author | Veronelli Giona |
| author_facet | Veronelli Giona |
| author_sort | Veronelli Giona |
| collection | DOAJ |
| description | We 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. |
| first_indexed | 2024-12-19T22:23:36Z |
| format | Article |
| id | doaj.art-384d70b02201411e8571c4b6987d5af1 |
| institution | Directory Open Access Journal |
| issn | 2299-3274 |
| language | English |
| last_indexed | 2024-12-19T22:23:36Z |
| publishDate | 2018-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Analysis and Geometry in Metric Spaces |
| spelling | doaj.art-384d70b02201411e8571c4b6987d5af12022-12-21T20:03:33ZengDe GruyterAnalysis and Geometry in Metric Spaces2299-32742018-11-016114616410.1515/agms-2018-0008agms-2018-0008Scalar Curvature via Local ExtentVeronelli Giona0Université Paris 13, Sorbonne Paris Cité, LAGA, avenue Jean- Baptiste ClémentVilletaneuse, FranceWe 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.https://doi.org/10.1515/agms-2018-0008scalar curvatureq-extentsurfaces with bounded integral curvaturealexandrov spaces |
| spellingShingle | Veronelli Giona Scalar Curvature via Local Extent Analysis and Geometry in Metric Spaces scalar curvature q-extent surfaces with bounded integral curvature alexandrov spaces |
| title | Scalar Curvature via Local Extent |
| title_full | Scalar Curvature via Local Extent |
| title_fullStr | Scalar Curvature via Local Extent |
| title_full_unstemmed | Scalar Curvature via Local Extent |
| title_short | Scalar Curvature via Local Extent |
| title_sort | scalar curvature via local extent |
| topic | scalar curvature q-extent surfaces with bounded integral curvature alexandrov spaces |
| url | https://doi.org/10.1515/agms-2018-0008 |
| work_keys_str_mv | AT veronelligiona scalarcurvaturevialocalextent |