Squeezing Lagrangian tori in dimension 4 (Q2214031)

Summary: Let \(\mathbb{C}^2\) be the standard symplectic vector space and \(L(a,b) \subset\mathbb{C}^2\) be the product Lagrangian torus, that is, a product of two circles of areas \(a\) and \(b\) in \(\mathbb{C}\). We give a complete answer to the question of finding the minimal ball into which these Lagrangians may be squeezed by a Hamiltonian flow. The result is that there is full rigidity when \(a\leq b\leq 2a\), which disappears almost completely when \(b > 2a\).