Morse-Smale characteristic foliations and convexity in contact manifolds

Breen, Joseph

doi:10.1090/proc/15484

Morse-Smale characteristic foliations and convexity in contact manifolds
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by Joseph Breen PDF

Proc. Amer. Math. Soc. 149 (2021), 3977-3989 Request permission

Abstract:

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.

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