Locally conformally symplectic deformation of Gromov non-squeezing

TL;DR

This paper extends the Gromov non-squeezing theorem to locally conformally symplectic (lcs) structures, generalizing symplectic and contact geometries, and discusses related conjectures and questions in lcs geometry.

Contribution

It provides a deformation theoretic extension of non-squeezing to lcs structures and proposes an analogue of contact non-squeezing in lcs geometry.

Findings

Extended non-squeezing to lcs structures

Proposed conjecture for lcs contact non-squeezing

Discussed related open questions in lcs geometry

Abstract

We prove one deformation theoretic extension of the Gromov non-squeezing phenomenon to $lcs$ structures, or locally conformally symplectic structures, which suitably generalize both symplectic and contact structures. We also conjecture an analogue in $lcs$ geometry of contact non-squeezing of Eliashberg-Polterovich and discuss other related questions.