A Cheeger type finiteness theorem for Finsler manifolds

TL;DR

This paper proves a Cheeger type finiteness theorem for Berwald Finsler manifolds by analyzing injectivity and convex radii, establishing estimates, and demonstrating the existence of a center of mass.

Contribution

It introduces a Cheeger type finiteness theorem for Berwald manifolds, including new estimates on injectivity radii and the existence of a center of mass.

Findings

Cheeger type estimate on injectivity radii for Finsler manifolds

Existence of the center of mass in Berwald manifolds

Finiteness results for classes of Berwald manifolds

Abstract

In this paper, we mainly establish a Cheeger type finiteness theorem for Berwald manifolds. In order to do this, we study the injectivity radius and the convex radius of a Finsler manifold. A Cheeger type estimate on injectivity radii for Finsler manifolds is given and the existence of the center of mass of a Berwald manifold is proved.