# Squeezing Lagrangian tori in dimension 4

### Richard Hind

University of Notre Dame, USA### Emmanuel Opshtein

Université de Strasbourg, France

## Abstract

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 $b > 2a$.

## Cite this article

Richard Hind, Emmanuel Opshtein, Squeezing Lagrangian tori in dimension 4. Comment. Math. Helv. 95 (2020), no. 3, pp. 535–567

DOI 10.4171/CMH/496