On the Gromov width of complements of Lagrangian tori

An integral product Lagrangian torus in the standard symplectic \(\mathbb{C}^2\) is defined to be a subset \(\{ \pi|z_1|^2 = k, \, \pi|z_2|^2 =l \}\) with \(k,l \in \mathbb{N}\). Let \(\mathcal{L}\) be the union of all integral product Lagrangian tori. We compute the Gromov width of complements \(B(...

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Bibliographic Details
Published inarXiv.org
Main Author Hind, Richard
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 06.05.2024
Subjects
Toruses
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Summary:An integral product Lagrangian torus in the standard symplectic \(\mathbb{C}^2\) is defined to be a subset \(\{ \pi|z_1|^2 = k, \, \pi|z_2|^2 =l \}\) with \(k,l \in \mathbb{N}\). Let \(\mathcal{L}\) be the union of all integral product Lagrangian tori. We compute the Gromov width of complements \(B(R) \setminus \mathcal{L}\) for some small \(R\), where \(B(R)\) denotes the round ball of capacity \(R\).
ISSN:2331-8422