### COMPARISON THEOREMS IN FINSLER GEOMETRY WITH WEIGHTED CURVATURE BOUNDS AND RELATED RESULTS

Wu, Bing-Ye

• 투고 : 2014.08.26
• 발행 : 2015.05.01
• 6 3

#### 초록

We first extend the notions of weighted curvatures, including the weighted flag curvature and the weighted Ricci curvature, for a Finsler manifold with given volume form. Then we establish some basic comparison theorems for Finsler manifolds with various weighted curvature bounds. As applications, we obtain some McKean type theorems for the first eigenvalue of Finsler manifolds, some results on weighted curvature and fundamental group for Finsler manifolds, as well as an estimation of Gromov simplicial norms for reversible Finsler manifolds.

#### 키워드

Finsler manifold;weighted flag curvature;weighted Ricci curvature;first eigenvalue;fundamental group

#### 참고문헌

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#### 피인용 문헌

1. A note on Berwald eikonal equation vol.766, 2016, https://doi.org/10.4134/JKMS.2015.52.3.603

#### 과제정보

연구 과제 주관 기관 : Natural Science Foundation of China