5 problems

Loose Legendrian rigidity conjecture. The Legendrian $\varphi_\infty(\Lambda)$ is still loose.

Legendrian Gauss-map rigidity conjecture. The diagram relating the Lagrangian Gauss maps of $\Lambda$ and $\varphi_\infty(\Lambda)$ commutes:

Let $\alpha$ be a contact form on the standard contact sphere $(S^{2n-1},\xi_{\mathrm{std}})$. A Reeb chord of a closed Legendrian submanifold $\Lambda$ is a Reeb trajectory of…

Let $(M,d\lambda)$ be an exact symplectic manifold, and let $L$ be a closed exact Lagrangian submanifold with vanishing Chekanov–Hofer metric. Let $\Lambda$ be the Legendrian lift…

Non-degeneracy conjecture. The $\alpha$-metric $\delta_{\alpha}$ on $\mathcal L(N)$ is non-degenerate.