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Abstract
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.
Keywords
Finsler manifold
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distortion
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S-curvature
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weighted Ricci curvature
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comparison theorem
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Songting YIN.
Comparison theorems on Finsler manifolds with weighted Ricci curvature bounded below.
Front. Math. China, 2018, 13(2): 435-448 DOI:10.1007/s11464-018-0692-1
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