A Cheeger type finiteness theorem for Finsler manifolds

作者: Yibing Shen , Wei Zhao

DOI:

关键词:

摘要: In this paper, we mainly establish a Cheeger type finiteness theorem for Berwald manifolds. order to do this, study the injectivity radius and convex of Finsler manifold. A estimate on radii manifolds is given existence center mass manifold proved.

参考文章(13)
Uwe Abresch, Wolfgang T. Meyer, Injectivity Radius Estimates and Sphere Theorems Comparison Geometry, 1997, ISBN 0-521-59222-4, págs. 1-47. pp. 1- 47 ,(1997)
Ernst Heintze, Hermann Karcher, A general comparison theorem with applications to volume estimates for submanifolds Annales Scientifiques De L Ecole Normale Superieure. ,vol. 11, pp. 451- 470 ,(1978) , 10.24033/ASENS.1354
Daniel Egloff, Uniform Finsler Hadamard manifolds Annales De L Institut Henri Poincare-physique Theorique. ,vol. 66, pp. 323- 357 ,(1997)
Dmitri Burago, Yuri Burago, Sergei Ivanov, A Course in Metric Geometry ,(2001)
Hans-Bert Rademacher, A sphere theorem for non-reversible Finsler metrics Mathematische Annalen. ,vol. 328, pp. 373- 387 ,(2004) , 10.1007/S00208-003-0485-Y
Hans-Bert Rademacher, The length of a shortest geodesic loop Comptes Rendus Mathematique. ,vol. 346, pp. 763- 765 ,(2008) , 10.1016/J.CRMA.2008.06.001
Wei Zhao, A Lower Bound for the Length of Closed Geodesics on a Finsler Manifold Canadian Mathematical Bulletin. ,vol. 57, pp. 194- 208 ,(2014) , 10.4153/CMB-2012-035-8
Jeff Cheeger, FINITENESS THEOREMS FOR RIEMANNIAN MANIFOLDS. American Journal of Mathematics. ,vol. 92, pp. 61- 74 ,(1970) , 10.2307/2373498
Wei Zhao, Yibing Shen, A Universal Volume Comparison Theorem for Finsler Manifolds and Related Results Canadian Journal of Mathematics. ,vol. 65, pp. 1401- 1435 ,(2013) , 10.4153/CJM-2012-053-4