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Local equivalence problem for Levi flat hypersurfaces

Author: Giuseppe Della Sala
Journal: Proc. Amer. Math. Soc. 139 (2011), 2449-2461
MSC (2010): Primary 32V40
Published electronically: December 3, 2010
MathSciNet review: 2784811
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Abstract: In this paper we consider germs of smooth Levi flat hypersurfaces, under the following notion of local equivalence: $ S_1\sim 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.

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Giuseppe Della Sala
Affiliation: Fakultät für Mathematik, Nordbergstrasse 15, University of Vienna, 1090 Vienna, Austria

Keywords: Levi flat hypersurface, equivalence problem
Received by editor(s): March 1, 2010
Received by editor(s) in revised form: June 17, 2010
Published electronically: December 3, 2010
Additional Notes: This paper was written while the author was a post-doc at the University of Vienna, supported by BMWF grant Y377. He is very grateful to B. Lamel for posing the question in the first place, for several conversations regarding the problem and for otherwise helping in many crucial ways. He also wishes to thank A. Saracco for discussing the topic and for a useful suggestion about section 3, and F. Forstneric for pointing out reference \cite{BD}.
Communicated by: Franc Forstneric
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.