Symplectic Camel theorems and ${\mathcal C}^0$-rigidity of coisotropic submanifolds

TL;DR

This paper investigates the ${ m C}^0$-rigidity of coisotropic submanifolds under symplectic homeomorphisms, demonstrating non-squeezing properties in various reduction scenarios, extending symplectic topology understanding.

Contribution

It provides new results on ${ m C}^0$-rigidity and non-squeezing for coisotropic submanifolds under symplectic homeomorphisms, linking symplectic topology and geometric analysis.

Findings

Symplectic homeomorphisms preserve non-squeezing in coisotropic reductions.

Several situations where ${ m C}^0$-rigidity applies to coisotropic submanifolds.

Extension of symplectic camel theorems to coisotropic settings.

Abstract

This paper deals with the ${\mathcal C}^0$-rigidity of the reduction of coiostropic submanifolds under the action of symplectic homeomorphism. More precisely, we exhibit several situations where a symplectic homeomorphism that takes a coisotropic submanifold to a smooth submanifold (which are then known to be coisotropic by a result of Humili\`ere-Leclercq-Seyfaddini) abides to the non-squeezing property in the reduction.