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

- Journal title : Journal of the Korean Mathematical Society
- Volume 52, Issue 3, 2015, pp.603-624
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2015.52.3.603

Title & Authors

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

Wu, Bing-Ye;

Wu, Bing-Ye;

Abstract

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.

Keywords

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

Language

English

Cited by

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