Scalar Curvature via Local Extent

IF 0.6 3区数学 Q2 MATHEMATICS Analysis and Geometry in Metric Spaces Pub Date : 2017-10-05 DOI:10.1515/agms-2018-0008

G. Veronelli

引用次数: 4

Abstract

Abstract 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.

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通过局部范围的标量曲率

摘要给出了光滑黎曼流形标量曲率的度量表征，分析了点的无限小邻域中(n + 1)个点之间的最大距离。由于这种表征纯粹是用距离函数表示的，它可以用来解决在非光滑度量空间上定义标量曲率的问题。在第二部分中，我们将讨论这个问题，特别关注具有有界积分曲率的Alexandrov空间和曲面。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Analysis and Geometry in Metric Spaces Mathematics-Geometry and Topology

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed. AGMS is devoted to the publication of results on these and related topics: Geometric inequalities in metric spaces, Geometric measure theory and variational problems in metric spaces, Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density, Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds. Geometric control theory, Curvature in metric and length spaces, Geometric group theory, Harmonic Analysis. Potential theory, Mass transportation problems, Quasiconformal and quasiregular mappings. Quasiconformal geometry, PDEs associated to analytic and geometric problems in metric spaces.

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