3 problems

Let $\alpha$ be a contact form inducing the standard contact structure $(S^3,\xi_{st})$, and let $\Lambda\subset S^3$ be a Legendrian submanifold. Arnold's chord conjecture. There…

Let a Legendrian be a Legendrian submanifold in the standard $3$-sphere, and let a Reeb vector field be a Reeb vector field for the contact structure. Arnol'd's Reeb chord conjectu…

Sheaf-theoretic Reeb chord bound conjecture. By combining the authors' technique with Asano--Ike's technique, the existence of such a sheaf should imply analogous results for Reeb…