Local equivalence problem for Levi flat hypersurfaces

Details Local equivalence problem for Levi flat hypersurfaces Local equivalence problem for Levi flat hypersurfaces

2010-03-08

arxiv.org/abs/1003.1592v1

Mathematics

Complex Variables

15 pages, no figures

Scientific paper

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 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 not equivalent hypersurfaces which are almost everywhere analytic.

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