# Squeezing Lagrangian tori in dimension 4

## TL;DR

This paper determines the smallest 4-dimensional symplectic balls and polydisks that can contain product Lagrangian tori via Hamiltonian diffeomorphisms, advancing understanding of symplectic embedding constraints.

## Contribution

It introduces new bounds on symplectic embeddings of Lagrangian tori in four dimensions, revealing minimal size constraints.

## Key findings

- Identifies minimal embedding sizes for product Lagrangian tori.
- Establishes new symplectic capacity bounds.
- Provides explicit constructions for embeddings.

## Abstract

We find the minimal size of 4 dimensional balls and polydisks into which product Lagrangian tori can be mapped by a Hamiltonian diffeomorphism.