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

Xinyue Cheng; Yalu Feng; Liulin Liu

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arXiv · 2507.08571

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

Xinyue Cheng·Yalu Feng·Liulin Liu

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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 ${\rm Ric}_{\infty}$. 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.

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BibTeX RIS

Xinyue Cheng, Yalu Feng, Liulin Liu. 2025-07-11. Isoperimetric inequality on Finsler metric measure manifolds with non-negative weighted Ricci curvature. https://arxiv.org/abs/2507.08571

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