On the Gromov width of complements of Lagrangian tori

Abstract

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 $R$.