# A symplectic embedding of the cube with minimal sections and a question by Schlenk

## TL;DR

The paper demonstrates a symplectic embedding of the open unit cube into a polydisc with optimal section areas and connected complements, addressing a question posed by F. Schlenk.

## Contribution

It provides a new symplectic embedding construction that achieves minimal section areas and connected complements, solving a specific open problem.

## Key findings

- Successful symplectic embedding with sharp section bounds
- Sections have minimal area as per the established bound
- Complement of each section remains path-connected

## Abstract

I prove that the open unit cube can be symplectically embedded into a longer polydisc in such a way that the area of each section satisfies a sharp bound and the complement of each section is path-connected. This answers a variant of a question by F. Schlenk.