We establish some comparison theorems on Finsler manifolds with curvature quadratic decay. As their applications, we obtain some optimal Cheeger–Gromov–Taylor type compact theorems, volume growth and Mckean type estimate for the first Dirichlet eigenvalue for such manifolds. Although we present the results for Finsler manifolds, they are all new results for Riemannian manifolds.

中文翻译：

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具有曲率二次衰减的黎曼-芬斯勒流形比较定理及其应用

我们建立了一些关于具有曲率二次衰减的 Finsler 流形的比较定理。作为它们的应用，我们获得了一些最优的 Cheeger-Gromov-Taylor 类型紧定理、体积增长和 Mckean 类型估计，用于此类流形的第一个 Dirichlet 特征值。虽然我们给出了 Finsler 流形的结果，但它们都是黎曼流形的新结果。