Liouville-type theorems for foliations with complex leaves

Giuseppe Della Sala[1]

  • [1] Institut fuer Mathematik Nordbergstrasse 15 1090 Wien (Autriche)

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 2, page 711-725
  • ISSN: 0373-0956

Abstract

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In this paper we discuss various problems regarding the structure of the foliation of some foliated submanifolds S of ℂ n , in particular Levi flat ones. As a general scheme, we suppose that S is bounded along a coordinate (or a subset of coordinates), and prove that the complex leaves of its foliation are planes.

How to cite

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Della Sala, Giuseppe. "Liouville-type theorems for foliations with complex leaves." Annales de l’institut Fourier 60.2 (2010): 711-725. <http://eudml.org/doc/116286>.

@article{DellaSala2010,
abstract = {In this paper we discuss various problems regarding the structure of the foliation of some foliated submanifolds $S$ of $\mathbb\{C\}^n$, in particular Levi flat ones. As a general scheme, we suppose that $S$ is bounded along a coordinate (or a subset of coordinates), and prove that the complex leaves of its foliation are planes.},
affiliation = {Institut fuer Mathematik Nordbergstrasse 15 1090 Wien (Autriche)},
author = {Della Sala, Giuseppe},
journal = {Annales de l’institut Fourier},
keywords = {Levi flat submanifolds; Liouville theorem; analytic multifunctions; analytic foliations; foliated hypersurface; Levi flat submanifold},
language = {eng},
number = {2},
pages = {711-725},
publisher = {Association des Annales de l’institut Fourier},
title = {Liouville-type theorems for foliations with complex leaves},
url = {http://eudml.org/doc/116286},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Della Sala, Giuseppe
TI - Liouville-type theorems for foliations with complex leaves
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 2
SP - 711
EP - 725
AB - In this paper we discuss various problems regarding the structure of the foliation of some foliated submanifolds $S$ of $\mathbb{C}^n$, in particular Levi flat ones. As a general scheme, we suppose that $S$ is bounded along a coordinate (or a subset of coordinates), and prove that the complex leaves of its foliation are planes.
LA - eng
KW - Levi flat submanifolds; Liouville theorem; analytic multifunctions; analytic foliations; foliated hypersurface; Levi flat submanifold
UR - http://eudml.org/doc/116286
ER -

References

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  10. Thomas Ransford, A new approach to analytic multifunctions, Set-Valued Anal. 7 (1999), 159-194 Zbl0994.30029MR1716030
  11. N. V. Shcherbina, On the polynomial hull of a graph, Indiana Univ. Math. J. 42 (1993), 477-503 Zbl0798.32026MR1237056
  12. Yum-Tong Siu, Nonexistence of smooth Levi-flat hypersurfaces in complex projective spaces of dimension ≥ 3 , Ann. of Math. (2) 151 (2000), 1217-1243 Zbl0980.53065MR1779568
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