On Closed Geodesics in Non-negatively Curved Finsler Structures with Large Volume Growth

Abstract

We prove that a reversible Berwaldian Finsler structure $\left(M,F\right)$ with base-independent non-negative radial flag curvature and large volume growth does not have any closed geodesics.

This paper is being withdrawn since our use of the comparison theorem for Finsler spaces was incorrect. However, we note that our conjecture was later proven by Martin Kell

References in corpus (4)

• Metric measure spaces with Riemannian Ricci curvature bounded from below
• The cut locus and distance function from a closed subset of a Finsler manifold
• Differential Harnack Estimates for heat Equation under Finsler-Ricci Flow
• A note on non-negatively curved Berwald spaces

Cited by in corpus (2)

• A note on non-negatively curved Berwald spaces
• The Caffarelli-Kohn-Nirenberg Inequalities on Metric Measure Spaces