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

IF 0.9 3区数学 Q2 MATHEMATICS

Analysis and Geometry in Metric Spaces Pub Date : 2020-07-01 DOI:10.1515/agms-2020-0131

Yufeng Lu, E. Minguzzi, Shin-ichi Ohta

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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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.