Comparison Theorems on Weighted Finsler Manifolds and Spacetimes with ϵ-Range

Pub Date : 2020-07-01 DOI:10.1515/agms-2020-0131
Yufeng Lu, E. Minguzzi, Shin-ichi Ohta
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引用次数: 14

Abstract

Abstract We establish the Bonnet–Myers theorem, Laplacian comparison theorem, and Bishop–Gromov volume comparison theorem for weighted Finsler manifolds as well as weighted Finsler spacetimes, of weighted Ricci curvature bounded below by using the weight function. These comparison theorems are formulated with ϵ-range introduced in our previous paper, that provides a natural viewpoint of interpolating weighted Ricci curvature conditions of different effective dimensions. Some of our results are new even for weighted Riemannian manifolds and generalize comparison theorems of Wylie–Yeroshkin and Kuwae–Li.
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关于加权Finsler流形与具有ε-范围的时空的比较定理
摘要我们利用权函数建立了加权Finsler流形的Bonnet–Myers定理、拉普拉斯比较定理和Bishop–Gromov体积比较定理,以及加权Ricci曲率有界的加权Finsleer时空。这些比较定理是用我们在前一篇文章中引入的ε-范围公式化的,这为不同有效维数的插值加权Ricci曲率条件提供了一个自然的观点。我们的一些结果甚至对于加权黎曼流形也是新的,并推广了Wylie–Yeroshkin和Kuwae–Li的比较定理。
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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