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

• Autorzy: Bing-Ye Wu
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 53B40: Finsler spaces and generalizations (areal metrics)
• 53C23: Global geometric and topological methods (\`a la Gromov); differential geometric analysis on metric spaces
• 58B20: Riemannian, Finsler and other geometric structures

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2014
• Tom: 112
• Numer: 3
• Strony: 267-286

Daty

wydano

2014

Twórcy

autor

Bing-Ye Wu

• Department of Mathematics, Minjiang University, Fuzhou, 350108 China

Identyfikatory

DOI

10.4064/ap112-3-5