Comparison Theorems on Weighted Finsler Manifolds and Spacetimes with <i>ϵ</i>-Range
Yufeng Lu, E. Minguzzi, Shin‐ichi Ohta
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.
Topics & Concepts
MathematicsRicci curvatureComparison theoremCurvaturePure mathematicsRange (aeronautics)Bounded functionLaplace operatorFunction (biology)Finsler manifoldRicci-flat manifoldMathematical analysisScalar curvatureGeometryBiologyMaterials scienceComposite materialEvolutionary biologyAdvanced Differential Geometry ResearchGeometric Analysis and Curvature FlowsCosmology and Gravitation Theories