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Comparison theorems on Riemannian–Finsler manifolds with curvature quadratic decay and their applications

Wu Bing Ye

Wu Bing Ye

Institution of Mathematics, Minjiang University, Fuzhou, Fujiang 350108, P. R. China

E-mail Address: wubingye@mju.edu.cn

E-mail Address: 569405943@qq.com

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https://doi.org/10.1142/S0129167X21500488Cited by:0 (Source: Crossref)

Abstract

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.

Communicated by Otis Chodosh

Keywords:

AMSC: 53C60, 53B40

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