A Bound on the Symplectic Systolic Ratio of Polytopes in Even-Dimensional Euclidean Space
Symplectic capacities are invariants in symplectic geometry that are used to obstruct symplectic embeddings. From a certain symplectic capacity, the Ekeland-Hofer-Zehnder capacity, one can construct the systolic ratio, which measures the difference in the capacity and the Euclidean volume. The systolic ratio of a unit ball is always 1. It was conjectured by Viterbo that the systolic ratio is bounded by 1. This conjecture was disproven by Haim-Kislev recently, and now it is open to determine wha…
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