2020/07/01 by Yufeng Lu, E. Minguzzi, Ettore Minguzzi +2
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Bounded function #Comparison theorem #Cosmology and Gravitation Theories #Curvature #Finsler manifold #Function (biology) #Geometric Analysis and Curvature Flows #Geometry #Laplace operator #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Pure mathematics #Range (aeronautics) #Ricci curvature #Ricci-flat manifold #Scalar curvature #math.DG #math.MG
paper · pdf · doi:10.1515/agms-2020-0131
published as Anal. Geom. Metr. Spaces 10 (2022) 1-30 · 39 pages; minor revisions, to appear in Anal. Geom. Metr. Spaces
openalex publication_date 2020/07/01 · arxiv created 2022/02/05 · arxiv updated 2022/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.