A Toponogov type triangle comparison theorem in Finsler geometry

TL;DR

This paper extends the Toponogov triangle comparison theorem to Finsler manifolds, providing new insights into curvature bounds and geometric properties in this broader setting.

Contribution

It establishes a Toponogov type triangle comparison theorem for Finsler manifolds under specific curvature and convexity conditions, advancing Finsler geometry theory.

Findings

Proves a triangle comparison theorem in Finsler geometry.

Identifies conditions under which the theorem holds.

Links radial curvature bounds to geometric properties.

Abstract

The aim of this article is to establish a Toponogov type triangle comparison theorem for Finsler manifolds, in the manner of radial curvature geometry. We consider the situation that the radial flag curvature is bounded below by the radial curvature function of a non-compact surface of revolution, the edge opposite to the base point is contained in a Berwald-like region, and that the Finsler metric is convex enough in the radial directions in that region.