On the strong Arnold chord conjecture for convex contact forms

Abstract The original Arnold chord conjecture states that every closed Legendrian submanifold of the standard contact sphere admits a Reeb chord with distinct endpoints with respect to any contact form. In this paper, we prove this conjecture for contact forms induced by strictly convex embeddings into under the assumption that minimal periodic Reeb orbits are of Morse–Bott type. We also provide a counterexample when the convexity condition is not satisfied.