Conjecture on coisotropic subvarieties of ample hypersurfaces

Let $X$ be an irreducible holomorphic symplectic manifold of dimension $2n$, and let $Y$ be a smooth ample hypersurface in $X$. A subvariety $Z\subset Y$ is coisotropic when its tangent spaces contain their symplectic orthogonals wherever they are defined. Coisotropic-subvariety conjecture. The hypersurface $Y$ contains no coisotropic subvariety except itself.

This would generalize the preceding nonexistence result for coisotropic subvarieties obtained as intersections with ample divisors. The conjecture concerns the restriction imposed by ampleness on the geometry of subvarieties inside holomorphic symplectic manifolds; no resolution is supplied in the source.