Isoperimetric inequality on Finsler metric measure manifolds with non-negative weighted Ricci curvature

2025/07/11 by Cheng, Xinyue, Feng, Yalu, Liu, Liulin
#53B40 #53C60 #58C35 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.08571

Abstract

In this paper, we define the volume entropy and the second Cheeger constant and prove a sharp isoperimetric inequality involving the volume entropy on Finsler metric measure manifolds with non-negative weighted Ricci curvature \rm Ric_∞. As an application, we prove a Cheeger-Buser type inequality for the first eigenvalue of Finsler Laplacian by using the volume entropy and the second Cheeger constant.

Citations

• Isoperimetric inequality for Finsler manifolds with non-negative Ricci curvature
• Sharp isoperimetric and Sobolev inequalities in spaces with nonnegative Ricci curvature
• A Universal Volume Comparison Theorem for Finsler Manifolds and Related Results
• Finsler interpolation inequalities
• Ricci curvature for metric-measure spaces via optimal transport
• Ricci curvature for metric-measure spaces via optimal transport

Related

• Isoperimetric inequality for Finsler manifolds with non-negative Ricci curvature
• On Finsler metric measure manifolds with integral weighted Ricci curvature bounds
• A sharp isoperimetric inequality in metric measure spaces with non-negative Ricci curvature
• Sharp and rigid isoperimetric inequality in metric measure spaces with non-negative Ricci curvature
• Some inequalities on Finsler manifolds with weighted Ricci curvature bounded below