Topology of complete Finsler manifolds with radial flag curvature bounded below

TL;DR

This paper extends comparison theorems to certain Finsler manifolds with radial flag curvature bounds, leading to results on their topological finiteness and diffeomorphism to Euclidean spaces.

Contribution

It introduces a Toponogov type triangle comparison theorem for Finsler manifolds with radial flag curvature bounds and applies it to topological classification.

Findings

Finiteness of topological type for the class of manifolds considered

Diffeomorphism to Euclidean spaces established

Extension of comparison theorems to Finsler geometry

Abstract

We recently established a Toponogov type triangle comparison theorem for a certain class of Finsler manifolds whose radial flag curvatures are bounded below by that of a von Mangoldt surface of revolution (arXiv:1205.3913). In this article, as its applications, we prove the finiteness of topological type and a diffeomorphism theorem to Euclidean spaces.