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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Local equivalence problem for Levi flat hypersurfaces
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by Giuseppe Della Sala PDF
Proc. Amer. Math. Soc. 139 (2011), 2449-2461 Request permission

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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Additional Information
  • Giuseppe Della Sala
  • Affiliation: Fakultät für Mathematik, Nordbergstrasse 15, University of Vienna, 1090 Vienna, Austria
  • MR Author ID: 794044
  • Email: giuseppe.dellasala@univie.ac.at, beppe.dellasala@gmail.com
  • 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
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 2449-2461
  • MSC (2010): Primary 32V40
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10746-3
  • MathSciNet review: 2784811