Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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COMPARISON THEOREMS IN FINSLER GEOMETRY WITH WEIGHTED CURVATURE BOUNDS AND RELATED RESULTS

  • Wu, Bing-Ye (Department of Mathematics Minjiang University)
  • Received : 2014.08.26
  • Published : 2015.05.01
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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.

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Acknowledgement

Supported by : Natural Science Foundation of China

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