On fundamental groups of Finsler manifolds

In this paper, we study the growth of fundamental groups of Finsler manifolds. Some relationships between the growth of fundamental groups and the volume growth of universal covers of Finsler manifolds are found. Some estimates of entropies and the number of generators of fundamental groups of Finsl...

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Bibliographic Details
Published in:	Science China. Mathematics Vol. 54; no. 9; pp. 1951 - 1964
Main Authors:	Shen, YiBing, Zhao, Wei
Format:	Journal Article
Language:	English
Published:	Heidelberg SP Science China Press 01-09-2011
Subjects:	Applications of Mathematics Mathematics Mathematics and Statistics fundamental group 37B40 entropy 53B40 quasi-isometry 53C23 14H30 Finsler manifold
Online Access:	Get full text
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Summary:	In this paper, we study the growth of fundamental groups of Finsler manifolds. Some relationships between the growth of fundamental groups and the volume growth of universal covers of Finsler manifolds are found. Some estimates of entropies and the number of generators of fundamental groups of Finsler manifolds are given. Moreover, the quasi-isometry and the geometric norm in Finsler geometry are considered.
ISSN:	1674-7283 1869-1862
DOI:	10.1007/s11425-011-4233-6