Local equivalence problem for Levi flat hypersurfaces

Abstract

In this paper we consider germs of smooth Levi flat hypersurfaces, under the following notion of local equivalence: S 1 ∼ S 2 if their one-sided neighborhoods admit a biholomorphism smooth up to the boundary. We introduce a simple invariant for this relation, which allows us to prove some characterizations of triviality (i.e. equivalence to the hyperplane). Then, we employ the same invariant to construct infinitely many non-trivial classes, including an infinite family of non-equivalent hypersurfaces which are almost everywhere analytic.