A Universal Volume Comparison Theorem for Finsler Manifolds and Related Results

2012/09/20 by Wei Zhao, Yibing Shen · 7 citations
Physics and Astronomy · Mathematics · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.4153/cjm-2012-053-4

Abstract

Abstract In this paper, we establish a universal volume comparison theorem for Finsler manifolds and give the Berger–Kazdan inequality and Santalá's formula in Finsler geometry. Based on these, we derive a Berger–Kazdan type comparison theorem and a Croke type isoperimetric inequality for Finsler manifolds.

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• Unexpected Analytic Phenomena on Finsler Manifolds
• On the geometry of irreversible metric-measure spaces: Convergence, Stability and Analytic aspects
• Integral curvature bounds and diameter estimates on Finsler manifolds
• Sharp uncertainty principles on general Finsler manifolds
• Weighted Projective Ricci Curvature in Finsler Geometry
• Cheeger's constant and the first eigenvalue of a closed Finsler manifold
• Isoperimetric inequality on Finsler metric measure manifolds with non-negative weighted Ricci curvature

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• Comparison Theorems in Finsler Geometry and their Applications
• A comparison theorem for Finsler submanifolds and its applications
• Some inequalities on Finsler manifolds with weighted Ricci curvature bounded below
• Isoperimetric inequality on Finsler metric measure manifolds with non-negative weighted Ricci curvature
• Volume comparison theorems in Finsler spacetimes