Pseudoconvex and Disprisoning Homogeneous Sprays

TL;DR

This paper extends the concepts of pseudoconvexity and disprisonment from geodesics of linear connections to general homogeneous sprays, showing their joint stability in the space of all such sprays.

Contribution

It introduces a generalization of pseudoconvexity and disprisonment conditions to homogeneous sprays and proves their joint stability in the fine topology.

Findings

Pseudoconvexity and disprisonment are stable for homogeneous sprays.

The results extend classical geodesic properties to broader spray classes.

Joint stability holds for all degrees of homogeneity.

Abstract

The pseudoconvex and disprisoning conditions for geodesics of linear connections are extended to the solution curves of general homogeneous sprays. The main result is that pseudoconvexity and disprisonment are jointly stable in the fine topology on the space of all homogeneous sprays of any degree of homogeneity.