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

Bing-Ye Wu (2014)

Annales Polonici Mathematici

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.

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