On Lagrangian barriers and applications of Non-Squeezing

TL;DR

This paper demonstrates the existence of Lagrangian barriers in specific domains in symplectic space, utilizing the Non-Squeezing Theorem, and introduces new applications of symplectic invariants.

Contribution

It establishes new classes of Lagrangian barriers and provides novel applications of the Non-Squeezing and Symplectic Camel Theorems.

Findings

Existence of Lagrangian barriers in certain domains.

Applications of Non-Squeezing Theorem to new symplectic problems.

Introduction of new symplectic invariants or techniques.

Abstract

In this note we show the existence of Lagrangian barriers in a certain class of domains in $\mathbb{R}^{2n}$, including dual Lagrangian products and some ``sufficiently" round domains. Many of these results come as applications of the Non-Squeezing Theorem. We also give a new interesting application of the Non-Squeezing Theorem and the Symplectic Camel Theorem.