  We generalize a result of Giroux which says that a closed surface in a
contact $3$-manifold with Morse-Smale characteristic foliation is convex.
Specifically, we show that the result holds in contact manifolds of arbitrary
dimension. As an application, we show that a particular closed hypersurface
introduced by A. Mori is $C^{\infty}$-close to a convex hypersurface.
