Comparison Theorems in Finsler Geometry and their Applications

Details Comparison Theorems in Finsler Geometry and their Applications Comparison Theorems in Finsler Geometry and their Applications

2005-12-29

arxiv.org/abs/math/0512633v1

Mathematics

Differential Geometry

17 pages

Scientific paper

We prove Hessian comparison theorems, Laplacian comparison theorems and
volume comparison theorems of Finsler manifolds under various curvature
conditions. As applications, we derive Mckean type theorems for the first
eigenvalue of Finsler manifolds, as well as generalize a result on fundamental
group due to Milnor to Finsler manifolds.

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