On curvature bounds in Lorentzian length spaces

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-30 DOI:10.1112/jlms.12971

Tobias Beran, Michael Kunzinger, Felix Rott

引用次数: 0

Abstract

We introduce several new notions of (sectional) curvature bounds for Lorentzian pre-length spaces: On the one hand, we provide convexity/concavity conditions for the (modified) time separation function, and, on the other hand, we study four-point conditions, which are suitable also for the non-intrinsic setting. Via these concepts, we are able to establish (under mild assumptions) the equivalence of all previously known formulations of curvature bounds. In particular, we obtain the equivalence of causal and timelike curvature bounds as introduced by Kunzinger and Sämann.

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论洛伦兹长度空间中的曲率边界

我们为洛伦兹前长空间引入了几个新的（截面）曲率边界概念：一方面，我们为（修正的）时间分离函数提供了凸性/凹性条件；另一方面，我们研究了四点条件，这些条件也适用于非本征结构。通过这些概念，我们能够（在温和的假设条件下）建立之前已知的所有曲率边界公式的等价性。特别是，我们得到了 Kunzinger 和 Sämann 提出的因果曲率边界和时间曲率边界的等价性。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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