We make the elementary observation that the Lagrangian submanifolds of Cn, n≥3, constructed by Ekholm, Eliashberg, Murphy and Smith are non-uniruled and, moreover, have infinite relative Gromov width. The construction of these submanifolds involve exact Lagrangian caps, which obviously are non-uniruled in themselves. This property is also used to show that if a Legendrian submanifold inside a contactisation admits an exact Lagrangian cap, then its Chekanov–Eliashberg algebra is acyclic.
This work was partially supported by the ERC starting grant of Frédéric Bourgeois StG-239781-ContactMath.
"Exact Lagrangian caps and non-uniruled Lagrangian submanifolds." Ark. Mat. 53 (1) 37 - 64, April 2015. https://doi.org/10.1007/s11512-014-0202-y