Sharp systolic inequalities for rotationally symmetric 2-orbifolds (Q2111944)

The aim of systolic geometry is the investigation of relations between the length of shortest closed geodesics and the volume of the ambient space. The systole of a Riemannian 2-sphere is defined as the length of its shortest nontrivial closed geodesic. Its systolic ratio is the square of the systole divided by the sphere's area, which can become arbitrarily small. A Riemannian metric on the 2-sphere is called Zoll if all its prime geodesics are closed and have the same length. A (geodesic) flow (and its defining metric) is called Besse, if all its orbits are periodic. The aim of the present paper is to characterize rotationally symmetric Besse metrics on a given spindle 2-orbifold as global maximizers of some systolic ratio among rotationally symmetric metrics, generalizing the result of [\textit{A. Abbondandolo} et al., Trans. Am. Math. Soc. 374, No. 3, 1815--1845 (2021; Zbl 1460.53037)]. Spindles are Besse orbifolds which can be constructed as surfaces of revolution homeomorphic to two-sphere with two cyclic orbifold singularities