# On the existence of closed geodesics on 2-orbifolds

## TL;DR

This paper proves that every compact Riemannian 2-orbifold contains infinitely many closed geodesics of positive length, extending the understanding of geodesic existence in orbifold geometry.

## Contribution

It establishes the existence of infinitely many closed geodesics on all compact Riemannian 2-orbifolds, a significant generalization of classical results for manifolds.

## Key findings

- Existence of infinitely many closed geodesics on compact Riemannian 2-orbifolds
- Extension of geodesic existence results from manifolds to orbifolds
- Positive length geodesics are guaranteed on all such orbifolds

## Abstract

We show that on every compact Riemannian 2-orbifold there exist infinitely many closed geodesics of positive length.