Comparison theorems in Finsler geometry and their applications. (English) Zbl 1111.53060
Comparison results in Riemannian geometry are useful in several important studies. The paper under review is devoted to generalizations of these tools to Finsler geometry. Namely, Hessian comparison, Laplacian comparison and volume comparison theorems are proved under appropriate curvature conditions. Two very interesting applications are obtained: McKean type theorems for the first eigenvalue of a Finsler manifold and a Milnor type result on the growth of the fundamental group.
Reviewer: Radu Miron (Iaşi)
MSC:
| 53C60 | Global differential geometry of Finsler spaces and generalizations (areal metrics) |
| 53B40 | Local differential geometry of Finsler spaces and generalizations (areal metrics) |
Keywords:
Finsler manifold; comparison theorem; fundamental group; volume comparison; Laplacian comparison; Hessian comparison,References:
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