Solution (source code)

= Solution

Again take a symplectic two-sphere, but let $L$ be a small latitude bounding a cap of area strictly below half the total area. A rotation carrying that cap to a disjoint cap carries $L$ to a disjoint Lagrangian circle. Rotations of the symplectic sphere are flows of <Hamiltonian vector fields>; for rotation about an axis, a height function is a <Hamiltonian function>. Thus this rotation is a <Hamiltonian isotopy>, and $L$ is Hamiltonian displaceable.