The strong Viterbo conjecture and various flavours of duality in Lagrangian products
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911060071546880 |
|---|---|
| author | Vicente, Alejandro |
| author_facet | Vicente, Alejandro |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07572 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The strong Viterbo conjecture and various flavours of duality in Lagrangian products Vicente, Alejandro Symplectic Geometry 53D05 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. |
| title | The strong Viterbo conjecture and various flavours of duality in Lagrangian products |
| topic | Symplectic Geometry 53D05 |
| url | https://arxiv.org/abs/2505.07572 |