Comparison Theorems on Weighted Finsler Manifolds and Spacetimes with ϵ-Range-Reference-Cited by-同舟云学术

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

Published:2022-01-01 Issue:1 Volume:10 Page:1-30
ISSN:2299-3274
Container-title:Analysis and Geometry in Metric Spaces
language:en
Short-container-title:

Author:

Lu Yufeng¹,Minguzzi Ettore²,Ohta Shin-ichi³

Affiliation:

1. Department of Mathematics , Osaka University , Osaka , Japan

2. Dipartimento di Matematica e Informatica “U . Dini”, Università degli Studi di Firenze , Firenze , Italy

3. Department of Mathematics , Osaka University , Osaka , Japan ; and RIKEN Center for Advanced Intelligence Project (AIP) , Nihonbashi , Tokyo , Japan

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Geometry and Topology,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/agms-2020-0131/pdf

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