Scalar Curvature via Local Extent-Reference-Cited by-同舟云学术

Scalar Curvature via Local Extent

Published:2018-11-01 Issue:1 Volume:6 Page:146-164
ISSN:2299-3274
Container-title:Analysis and Geometry in Metric Spaces
language:
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Author:

Veronelli Giona

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Geometry and Topology,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/agms-2018-0008/pdf

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