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Izv. RAN. Ser. Mat., 2017, Volume 81, Issue 5, Pages 150–164 (Mi izv8582)  

This article is cited in 2 scientific papers (total in 2 papers)

Dicritical singularities and laminar currents on Levi-flat hypersurfaces

S. I. Pinchuka, R. G. Shafikovb, A. B. Sukhovc

a Indiana University, USA
b University of Western Ontario, Canada
c Université de Lille

Abstract: We establish an effective criterion for a dicritical singularity of a real analytic Levi-flat hypersurface. The criterion is stated in terms of Segre varieties. As an application, we obtain a structure theorem for a certain class of currents in the non-dicritical case.

Keywords: Levi-flat set, dicritical singularity, foliation, current.

Funding Agency Grant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)
Labex
R. G. Shafikov is partially supported by the Natural Sciences and Engineering Research Council of Canada. A. B. Sukhov is partially supported by Labex CEMPI.


DOI: https://doi.org/10.4213/im8582

Full text: PDF file (544 kB)
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English version:
Izvestiya: Mathematics, 2017, 81:5, 1030–1043

Bibliographic databases:

Document Type: Article
UDC: 517.55
MSC: 37F75, 34M, 32S, 32D
Received: 15.06.2016
Revised: 08.01.2017

Citation: S. I. Pinchuk, R. G. Shafikov, A. B. Sukhov, “Dicritical singularities and laminar currents on Levi-flat hypersurfaces”, Izv. RAN. Ser. Mat., 81:5 (2017), 150–164; Izv. Math., 81:5 (2017), 1030–1043

Citation in format AMSBIB
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\paper Dicritical singularities and laminar currents on Levi-flat hypersurfaces
\jour Izv. RAN. Ser. Mat.
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\vol 81
\issue 5
\pages 150--164
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\vol 81
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\pages 1030--1043
\crossref{https://doi.org/10.1070/IM8582}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Ufa Math. J., 9:3 (2017), 172–185  mathnet  crossref  mathscinet  isi  elib  scopus
    2. A. Beltrán, A. Fernández-Pérez, H. Neciosup, “Existence of dicritical singularities of Levi-flat hypersurfaces and holomorphic foliations”, Geod. Dedic., 196:1 (2018), 35–44  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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