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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.07572 |
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Table of Contents:
- In this note we analyze normalized symplectic capacities for two different notions of duality in Lagrangian products. Let $Φ$ be a $n$-tuple of Young functions with Legendre transform $n$-tuple $Φ^*$ and $K_Φ$ the unit ball for the Luxemburg metric induced by $Φ$. We can consider the ``dual functional" Lagrangian product $K_Φ\times_LK_{Φ^*}$ and the usual polar dual Lagrangian product $K_Φ\times_L K_Φ^{\circ}$. We show that for the former, all normalized symplectic capacities agree, while for the latter, we give a lower bound depending on $Φ$. In particular, under certain conditions on the $n$-tuple $Φ$, we get that $c(K_Φ\times_L K_Φ^{\circ})=4$, for any normalized symplectic capacity, that is, the strong Viterbo conjecture holds.