The symplectic non-squeezing properties of mass subcritical Hartree equations

We prove the non-squeezing properties of all mass subcritical Hartree equations on Rd (d≥2). The result is achieved by elaborating and generalizing some of the techniques in [13], [14] by Killip-Visan-Zhang, and two major ingredients are the weak well-posedness for a sequence of changing equations and approximation to an infinite dimensional problem by finite dimensional problem.