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 $R$.