Volume comparison theorem for tubular neighborhoods of submanifolds in Finsler geometry and its applications
Volume 112 / 2014
Annales Polonici Mathematici 112 (2014), 267-286
MSC: Primary 53C23; Secondary 53B40,58B20.
DOI: 10.4064/ap112-3-5
Abstract
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.
