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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap112-3-5,
author = {Bing-Ye Wu},
title = {Volume comparison theorem for tubular neighborhoods of submanifolds in Finsler geometry and its applications},
journal = {Annales Polonici Mathematici},
volume = {111},
year = {2014},
pages = {267-286},
zbl = {1310.53064},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap112-3-5}
}
Bing-Ye Wu. Volume comparison theorem for tubular neighborhoods of submanifolds in Finsler geometry and its applications. Annales Polonici Mathematici, Tome 111 (2014) pp. 267-286. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap112-3-5/