Comparison Theorems in Finsler Geometry and their Applications

B.Y.Wu; Y.L.Xin

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Comparison Theorems in Finsler Geometry and their Applications

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arxiv math/0512633 v1 pith:44EORHZP submitted 2005-12-29 math.DG

B.Y.Wu , Y.L.Xin This is my paper

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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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