The paper “Inertial manifolds for the 3D Cahn-Hilliard equations with periodic boundary conditions“, co-authored by Anna Kostianko and Sergey Zelik, has been accepted for publication in Communications on Pure and Applied Analysis (CPAA).  In the paper, the existence of an inertial manifold for the 3D Cahn-Hilliard equation with periodic boundary conditions is verified using a proper extension of the so-called spatial averaging principle introduced by G. Sell and J. Mallet-Paret.  Moreover, the extra regularity of this manifold is also obtained.  A final form preprint can be downloaded here from the arXiv.