no. 2
Liouville-type theorems for foliations with complex leaves
Della Sala, Giuseppe1
1 Institut fuer Mathematik Nordbergstrasse 15 1090 Wien (Autriche)
Annales de l'Institut Fourier, Volume 60 (2010) no. 2, pp. 711-725.

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.

Dans cet article nous considérons différentes questions relatives à la structure du feuilletage de certaines sous-variétés S⊂ℂ n , en particulier les variétés Levi-plates. Comme schéma général, on suppose que S est bornée le long d’une coordonnée (ou d’un sous-ensemble des coordonnées), et on montre que les feuilles complexes de son feuilletage sont des plans.

DOI: 10.5802/aif.2537
Classification: 32V40
Keywords: Levi flat submanifolds, Liouville theorem, analytic multifunctions
Mot clés : sous-variétés Levi-plates, Théorème de Liouville, multifonctions analytiques

Della Sala, Giuseppe 1

1 Institut fuer Mathematik Nordbergstrasse 15 1090 Wien (Autriche) 
@article{AIF_2010__60_2_711_0,
     author = {Della Sala, Giuseppe},
     title = {Liouville-type theorems for foliations with complex leaves},
     journal = {Annales de l'Institut Fourier},
     pages = {711--725},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {60},
     number = {2},
     year = {2010},
     doi = {10.5802/aif.2537},
     mrnumber = {2667791},
     zbl = {1194.32026},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2537/}
}
TY  - JOUR
AU  - Della Sala, Giuseppe
TI  - Liouville-type theorems for foliations with complex leaves
JO  - Annales de l'Institut Fourier
PY  - 2010
SP  - 711
EP  - 725
VL  - 60
IS  - 2
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.2537/
DO  - 10.5802/aif.2537
LA  - en
ID  - AIF_2010__60_2_711_0
ER  - 
%0 Journal Article
%A Della Sala, Giuseppe
%T Liouville-type theorems for foliations with complex leaves
%J Annales de l'Institut Fourier
%D 2010
%P 711-725
%V 60
%N 2
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.2537/
%R 10.5802/aif.2537
%G en
%F AIF_2010__60_2_711_0
Della Sala, Giuseppe. Liouville-type theorems for foliations with complex leaves. Annales de l'Institut Fourier, Volume 60 (2010) no. 2, pp. 711-725. doi : 10.5802/aif.2537. https://aif.centre-mersenne.org/articles/10.5802/aif.2537/

[1] Barrett, D. E.; Fornæss, J. E. On the smoothness of Levi-foliations, Publ. Mat., Volume 32 (1988) no. 2, pp. 171-177 | MR | Zbl

[2] Barrett, David E.; Inaba, Takashi On the topology of compact smooth three-dimensional Levi-flat hypersurfaces, J. Geom. Anal., Volume 2 (1992) no. 6, pp. 489-497 | MR | Zbl

[3] Bryant, Robert L. Levi-flat minimal hypersurfaces in two-dimensional complex space forms, Lie groups, geometric structures and differential equations—one hundred years after Sophus Lie (Kyoto/Nara, 1999) (Adv. Stud. Pure Math.), Volume 37, Math. Soc. Japan, Tokyo, 2002, pp. 1-44 | MR | Zbl

[4] Fornaess, John Erik; Stout, Edgar Lee Polydiscs in complex manifolds, Math. Ann., Volume 227 (1977) no. 2, pp. 145-153 | DOI | MR | Zbl

[5] Lins Neto, Alcides A note on projective Levi flats and minimal sets of algebraic foliations, Ann. Inst. Fourier (Grenoble), Volume 49 (1999) no. 4, pp. 1369-1385 | DOI | Numdam | MR | Zbl

[6] Lupacciolu, Guido; Tomassini, Giuseppe An extension theorem for CR-functions, Ann. Mat. Pura Appl. (4), Volume 137 (1984), pp. 257-263 | DOI | MR | Zbl

[7] Ohsawa, Takeo On the Levi-flats in complex tori of dimension two, Publ. Res. Inst. Math. Sci., Volume 42 (2006) no. 2, pp. 361-377 | DOI | MR | Zbl

[8] Oka, Kiyosi Note sur les familles de fonctions analytiques multiformes, J. Sci. Hiroshima Univ. Ser. A, Volume 4 (1934), pp. 93-98 | Zbl

[9] Pugh, Charles C. The Morse-Sard theorem with mixed differentiability, Indiana Univ. Math. J., Volume 40 (1991) no. 4, pp. 1387-1396 | DOI | MR | Zbl

[10] Ransford, Thomas A new approach to analytic multifunctions, Set-Valued Anal., Volume 7 (1999) no. 2, pp. 159-194 | DOI | MR | Zbl

[11] Shcherbina, N. V. On the polynomial hull of a graph, Indiana Univ. Math. J., Volume 42 (1993) no. 2, pp. 477-503 | DOI | MR | Zbl

[12] Siu, Yum-Tong Nonexistence of smooth Levi-flat hypersurfaces in complex projective spaces of dimension ≥3, Ann. of Math. (2), Volume 151 (2000) no. 3, pp. 1217-1243 | DOI | MR | Zbl

[13] Slodkowski, Zbigniew Analytic set-valued functions and spectra, Math. Ann., Volume 256 (1981) no. 3, pp. 363-386 | DOI | MR | Zbl

[14] Stolzenberg, Gabriel Uniform approximation on smooth curves, Acta Math., Volume 115 (1966), pp. 185-198 | DOI | MR | Zbl

Cited by Sources: