# Bernig, A (2003). *Scalar curvature of definable CAT-spaces.* Advances in Geometry, 3(1):23-43.

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## Abstract

We study the scalar curvature measure for sets belonging to o-minimal structures (e.g. semialgebraic or subanalytic sets) from the viewpoint of metric dierential geometry. Theorem: Let S be a compact connected definable pseudo-manifold with curvature bounded from above, then the singular part of the scalar curvature measure is non-positive. The topo- logical restrictions cannot be removed, as is shown in examples.

Item Type: | Journal Article, refereed, original work |
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Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

DDC: | 510 Mathematics |

Language: | English |

Date: | 2003 |

Deposited On: | 29 Nov 2010 16:26 |

Last Modified: | 27 Nov 2013 19:56 |

Publisher: | De Gruyter |

ISSN: | 1615-715X |

Free access at: | Related URL. An embargo period may apply. |

Publisher DOI: | 10.1515/advg.2003.003 |

Related URLs: | http://www.ams.org/mathscinet-getitem?mr=1956586 http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1028.53031 http://www.math.ethz.ch/EMIS/journals/AG/3-1/3_23.pdf |

Citations: | Web of Science®. Times Cited: 7 Google Scholar™ |

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