Volume comparison theorem for tubular neighborhoods of submanifolds in Finsler geometry and its applications
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.