A Finsler counterexample to the Croke conjecture for the systolic ratio on the 2-sphere

Guillaume Buro, Louis Merlin

We exhibit a Finsler metric on the 2-sphere whose systolic (Holmes-Thompson) ratio is $\frac{4\pi }{3}$. This is bigger than the conjectured maximal Riemannian systolic ratio of $2\sq…