A Finsler counterexample to the Croke conjecture for the systolic ratio on the 2-sphere
Abstract
We exhibit a Finsler metric on the 2-sphere whose systolic (Holmes-Thompson) ratio is 4π3. This is bigger than the conjectured maximal Riemannian systolic ratio of 23 achieved by the Calabi-Croke metric. The construction of the Finsler metric is heavily inspired by a paper of Cossarini-Sabourau.
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