Arkiv för Matematik

, Volume 44, Issue 1, pp 87–91 | Cite as

A contractible Levi-flat hypersurface which is a determining set for pluriharmonic functions

Article
  • 37 Downloads

Abstract

We find a real analytic Levi-flat hypersurface in C2 containing a bounded contractible domain which is a determining set for pluriharmonic functions.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. 1.
    Barrett, D. E., Global convexity properties of some families of three-dimensional compact Levi-flat hypersurfaces, Trans. Amer. Math. Soc.332 (1992), 459–474.Google Scholar
  2. 2.
    Barrett, D. E. and Fornæss, J. E., On the smoothness of Levi-foliations, Publ. Mat.32 (1988), 171–177.Google Scholar
  3. 3.
    Candel, A. and Conlon, L., Foliations I, Grad. Stud. Math. 23, Amer. Math. Soc., Providence, RI, 2000.Google Scholar
  4. 4.
    Forstnerič, F. and Laurent-Thiébaut, C., Stein compacts in Levi-flat hypersurfaces, Trans. Amer. Math. Soc., to appear.Google Scholar
  5. 5.
    Godbillon, C., Dynamical Systems on Surfaces, Springer, Berlin–New York, 1983.Google Scholar
  6. 6.
    Godbillon, C., Feuilletages. Études Géométriques, Birkhäuser, Basel, 1991.Google Scholar
  7. 7.
    Haefliger, A., Structures feuilletées et cohomologie à valeur dans un faisceau de groupoïdes, Comment. Math. Helv.32 (1958), 248–329.Google Scholar
  8. 8.
    Haefliger, A. and Reeb, G., Variétés (non séparées) à un dimension et structures feuilletées du plan, Enseign. Math.3 (1957), 107–125.Google Scholar
  9. 9.
    Kamke, E., Über die partielle Differentialgleichung fzx+gzy=h, Math. Z.41 (1936), 56–66; ibid.42 (1937), 287–300.Google Scholar
  10. 10.
    Tomassini, G., Extension of CR-functions, in Seminar on Deformations (Łódź/Warsaw, 1982/84), Lect. Notes Math. 1165, pp. 294–301, Springer, Berlin, 1985.Google Scholar
  11. 11.
    Wazewsky, T., Sur l’équation Pp+Qq=0, Mathematica8 (1934), 103–116; ibid.9 (1935), 179–182.Google Scholar

Copyright information

© Institut Mittag-Leffler 2006

Authors and Affiliations

  1. 1.Institute of Mathematics, Physics and MechanicsUniversity of LjubljanaLjubljanaSlovenia

Personalised recommendations