Comparison theorems in Riemann-Finsler geometry with line radial integral curvature bounds and related results
J. Korean Math. Soc. 2019 Vol. 56, No. 2, 421-437
Published online 2019 Mar 01
Bing-Ye Wu
Minjiang University
Abstract : We establish some Hessian comparison theorems and volume comparison theorems for Riemann-Finsler manifolds under various line radial integral curvature bounds. As their applications, we obtain some results on first eigenvalue, Gromov pre-compactness and generalized Myers theorem for Riemann-Finsler manifolds under suitable line radial integral curvature bounds. Our results are new even in the Riemannian case.
Keywords : extreme volume form, Finsler manifold, Gromov pre-compact\-ness, first eigenvalue, diameter
MSC numbers : Primary 53C60; Secondary 53B40
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