A globalization for non-complete but geodesic spaces

TL;DR

This paper proves that geodesic spaces with local Alexandrov curvature bounds retain these bounds globally upon completion, extending local geometric properties to the entire space.

Contribution

It establishes that local curvature bounds in geodesic spaces are preserved globally after completion, a significant extension of Alexandrov geometry theory.

Findings

Completion of locally curved geodesic spaces maintains the same curvature bounds

Local curvature conditions imply global bounds in geodesic spaces

Results extend Alexandrov geometry to non-complete spaces

Abstract

I show that if a geodesic space has curvature bounded below locally in the sense of Alexandrov then its completion has the same lower curvature bound globally.