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Locally conformally symplectic deformation of Gromov non-squeezing

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Abstract

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

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Acknowledgements

I am grateful to Kevin Sackel, Richard Hind, and Vestislav Apostolov for related discussions, as well as the referee for nice suggestions.

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  1. University of Colima, CUICBAS, Colima, Mexico

    Yasha Savelyev

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  1. Yasha Savelyev
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Correspondence to Yasha Savelyev.

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Savelyev, Y. Locally conformally symplectic deformation of Gromov non-squeezing. Arch. Math. 122, 95–108 (2024). https://doi.org/10.1007/s00013-023-01922-6

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  • DOI: https://doi.org/10.1007/s00013-023-01922-6

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