Comparison theorems on Finsler manifolds with weighted Ricci curvature bounded below
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We obtain the Laplacian comparison theorem and the Bishop-Gromov comparison theorem on a Finsler manifold with the weighted Ricci curvature Ric∞ bounded below. As applications, we prove that if the weighted Ricci curvature Ric∞ is bounded below by a positive number, then the manifold must have finite fundamental group, and must be compact if the distortion is also bounded. Moreover, we give the Calabi-Yau linear volume growth theorem on a Finsler manifold with nonnegative weighted Ricci curvature.
KeywordsFinsler manifold distortion S-curvature weighted Ricci curvature comparison theorem
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This work was supported in part by the Natural Science Foundation of Anhui Province (No. 1608085MA03) and the National Natural Science Foundation of China (Grant No. 11471246).
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