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math.DG2026

The Rigidity of the closed three dimensional regular Landsberg metrics

Jianyu Mao, Linfeng Zhou

The Landsberg Berwald conjecture asks whether every regular Landsberg metric is Berwald. We settle this conjecture for closed three-dimensional manifolds: every smooth strongly con…

math.DG2025

A Weighted Llarull Type Theorem and its applications

Linfeng Zhou, Guangrui Zhu

This paper generalizes Llarull's classical scalar curvature rigidity theorem to the setting of weighted manifolds with P-scalar curvature. More precisely, we prove the refinement o…

math.DG2021

A uniformization theorem in complex Finsler geometry

Ningwei Cui, Jinhua Guo, Linfeng Zhou

In complex Finsler geometry, an open problem is: does there exist a weakly Kähler Finsler metric which is not Kähler? In this paper, we give an affirmative answer to this open prob…

math.DG2017

The isoperimetric problem in the 2-dimensional Finsler space forms with k = 0. II

Mengqing Zhan, Linfeng Zhou

This paper is a continuation of the second author's previous work. We investigate the isoperimetric problem in the 2-dimensional Finsler space form with by us…

math.DG2017

The isoperimetric problem in the 2-dimensional Finsler space forms with k = 0. I

Linfeng Zhou

In this paper, the isoperimetric problem in the 2-dimensional Finsler space form with k = 0 by using the Busemann-Hausdorff area is investigated. We prove that the c…

math.DG2014

The spherically symmetric Finsler metrics with isotropic S-curvature

Linfeng Zhou

In this paper, we investigate the spherically symmetric Finsler metrics with isotropic S-curvature and obtain a characterized equation. As an application, we prove that these metri…