Geodesic
Volume comparison theorem for tubular neighborhoods of submanifolds in Finsler geometry and its applications
Bing-Ye Wu1
1 Department of Mathematics Minjiang University Fuzhou, 350108 China
Annales Polonici Mathematici, Tome 112 (2014) no. 3, pp. 267-286 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We consider the distance to compact submanifolds and study volume comparison for tubular neighborhoods of compact submanifolds. As applications, we obtain a lower bound for the length of a closed geodesic of a compact Finsler manifold. When the Finsler metric is reversible, we also provide a lower bound of the injectivity radius. Our results are Finsler versions of Heintze–Karcher's and Cheeger's results for Riemannian manifolds.
DOI : 10.4064/ap112-3-5
Keywords: consider distance compact submanifolds study volume comparison tubular neighborhoods compact submanifolds applications obtain lower bound length closed geodesic compact finsler manifold finsler metric reversible provide lower bound injectivity radius results finsler versions heintze karchers cheegers results riemannian manifolds

Bing-Ye Wu 1

1 Department of Mathematics Minjiang University Fuzhou, 350108 China 
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Bing-Ye Wu. Volume comparison theorem for tubular neighborhoods of submanifolds in Finsler geometry and its applications. Annales Polonici Mathematici, Tome 112 (2014) no. 3, pp. 267-286. doi: 10.4064/ap112-3-5

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