Reeb chords of Lagrangian slices

Abstract

In this short note we observe that the boundary of a properly embedded compact exact Lagrangian sub-manifolds in a subcritical Weinstein domain $X$ necessarily admits Reeb chords. The existence of this Reeb chords either follows from an obstruction to the deformation of the boundary to a cylinder over a Legendrian sub-manifold or from the fact that the wrapped Floer homology of the Lagrangian vanishes once this boundary have been "collared".

v2: incorporated some referee comments which expand exposition, section 4 is now section 2. To appear in the Journal of fixed point theory and applications, Viterbo's 60th anniversary edition