Legendrians with vanishing Shelukhin–Chekanov–Hofer metric

We show that the Legendrian lift of an exact, displaceable Lagrangian has vanishing Shelukhin–Chekanov–Hofer pseudo-metric by lifting an argument due to Sikorav to the contactization. In particular, this proves the existence of such Legendrians, providing counterexamples to a conjecture of Rosen and Zhang.

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This work is partially supported by the Knut and AliceWallenberg Foundation, grant KAW2020.0307.

Received 1 February 2023

Received revised 15 November 2023

Accepted 14 December 2023

Published 1 June 2024